Mysaa/TIPE2021
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Nouvel algorithme de décodage avec enregistrement dans un dictionnaire des syndromes

Browse Source 
Fin de la rédaction du dossier (manque encore des finitions)
This commit is contained in:
Mysaa 2021-06-02 15:12:22 +02:00
parent 2c825f16a8
commit 36875fc40a
9 changed files with 307 additions and 145 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

35
Code.ml
View File

@ -22,8 +22,8 @@
* on représente un vecteur dans F_2 par un entier dont la décomposition binaire correspond aux composantes du vecteur
* on représente une matrice par un liste d'entier, il s'agit de la liste de ses colonnes (qui sont donc des vecteurs)
*)
(*
#cd "/home/mysaa/Documents/Arbeiten/TIPE2021/";;
#load "Math.cmo";;
*)
@ -132,6 +132,37 @@ let decoder code z =
;;
(*** Décodage avec stockage des syndromes ***)
(* syndr est une fonction qui à un vecteur associe son syndrome.
En effet, la notion de syndrome dépend de quelle matrice H nous avons choisi.
Créer cette fonction ici permet de ne plus dépendre de la matrice H de code_lineaire *)
type classesLaterales = {syndr : Math.vecteur -> Math.vecteur;
erreur : Math.vecteur -> Math.vecteur;
babr : Math.vecteur Math.binabr};;
let genererClasses code =
let syndr = function z -> Math.produit code.h z in
let compacteur babr v = if BFeuille<>babr && not (appartenir code v)
then (print_int v;putWho babr (syndr v)) v false
else BFeuille in
let rec iter babr0 lst =
let svts = suivants code.n lst in
let babr = List.fold_left compacteur babr0 svts in
if babr<>BFeuille
then iter babr svts
else babr0 (*On a dépassé la capacité de correction*)
in
let babr = iter (put BFeuille 0 0) [0] in
let erreur = function z -> get babr z
in {syndr=syndr;erreur=erreur;babr=babr}
;;
let decoder2 classes z :vecteur=
let s = classes.syndr z in
let e = classes.erreur s in
z lxor e;;
end;;
(*************************************************************)

14
Code.mli
View File

@ -6,12 +6,22 @@ type t = {
g : Math.matrice;
h : Math.matrice; }
type code_lineaire = t
exception PasDansLeCodeException
val encoder : code_lineaire -> Math.vecteur -> Math.vecteur
val systematiqueFromRedondance : int -> int -> matrice -> code_lineaire
val systematiqueFromRedondance : int -> int -> Math.matrice -> code_lineaire
val distance_minimale : code_lineaire -> int
val decoder : code_lineaire -> int -> Math.vecteur
val decoder : code_lineaire -> Math.vecteur -> Math.vecteur
val appartenir : code_lineaire -> Math.vecteur -> bool
type classesLaterales = {
syndr : Math.vecteur -> Math.vecteur;
erreur : Math.vecteur -> Math.vecteur;
babr : Math.vecteur Math.binabr;
}
val genererClasses : t -> classesLaterales
val decoder2 : classesLaterales -> Math.vecteur -> Math.vecteur
end
module CCyclique :

1
CompteRendu/.gitignore vendored
View File

@ -6,3 +6,4 @@
*.toc
*.thm
svg-inkscape/
print_output_path.svg

25
CompteRendu/CompteRendu.tex
View File

@ -123,6 +123,7 @@
$$d_C \leqslant n+1-k$$
Enfin, on peut utiliser que la distance minimale d'un code linéaire est le nombre minimal de colonnes linéairement dépendantes de la matrice de contrôle $H$.
\end{theoreme}
Voici ici quelques concepts qui seront utiles au décodage.
@ -149,11 +150,10 @@
On définit le mot binaire associé au polynôme $P=\displaystyle\sum_{i=0}^{n-1}{a_i\cdotp X^i}$ comme étant le mot $a_0a_1\cdots a_{n-1}$. Le polynôme réciproquement associé à un mot binaire par ce procédé est appelé \textbf{représentation polynomiale} du mot.
\end{definition}
\begin{definition}[Polynôme générateur]
Un polynôme $P$ de $\FD\,[X]$ de degré $n-k$ est dit \textbf{générateur du code cyclique $C$ de paramètre $(k,n)$} lorsque $P | X^n + 1$ et que $(\sigma^i(w))_{i\in \llbracket 0,k-1\rrbracket}$ est une base de $C$ avec $\sigma$ l'opérateur de décalage binaire cyclique est $w$ le mot associé à $P$
\end{definition}
\begin{theoreme}[Théorème fondamental des codes cycliques]
Tout code cyclique admet un et un seul polynôme générateur.
Pour tout code cyclique $C$ de paramètres $(n,k)$, il existe un unique polynôme $g$ tel que le mot associé à $g$ engendre $C$ et que $g|X^n-1$. Ce polynôme est alors appelé \textbf{polynôme générateur du code cyclique $C$}.
On démontre que ce $g$ est alors de degré $n-k$ et que $(\sigma^i(w))_{i\in \llbracket 0,k-1\rrbracket}$ est une base de $C$ avec $\sigma$ l'opérateur de décalage binaire cyclique est $w$ le mot associé à $y$
\end{theoreme}
\begin{remarque}
@ -211,20 +211,25 @@
Nous avons ensuite écrit des fonctions permettant de manipuler les codes linéaires:
\begin{itemize}
\fsign{encoder}{code\_lineaire \into Math.vecteur \into Math.vecteur}{}
\fsign{encoder}{code\_lineaire \into vecteur \into vecteur}{k}
Encode le vecteur de $\FD^k$ suivant le code linéaire spécifié, il s'agit alors d'un simple produit avec la matrice génératrice.
\fsign{appartenir}{code_lineaire -> Math.vecteur -> bool}
\fsign{appartenir}{code\_lineaire -> vecteur -> bool}{n}
Renvoie \textit{vrai} si et seulement si le vecteur appartient au code, c'est à dire, si et seulement si $HX=0$ avec $H$ la matrice de contrôle et $X$ le vecteur de $\FD^n$ en question.
\fsign{distance\_minimale}{code\_lineaire -> int}{}
Renvoie la distance minimale du code, utilisée pour calculer les capacités de détéction et de correction du code (voir \ref{thCapacité})
\fsign{decoder}{code\_lineaire \into int \into Math.vecteur}{}
\fsign{distance\_minimale}{code\_lineaire -> int}{non}
Renvoie la distance minimale du code, utilisée pour calculer les capacités de détéction et de correction du code (voir \ref{thCapacité}). Le calcul s'effectue en recherchant le plus petit mot (au sens du poids) qui soit dans le code.
\fsign{decoder}{code\_lineaire \into vecteur \into Math.vecteur}{euhhhhhhhh}
Décode le mot de $\FD^n$ donné. L'algorithme recherche le mot le plus proche du mot recu qui soit dans le code et à une distance inferieure à la distance de correction. Si il est impossible de décoder, renvoie une exception du type \verb|IndecodableException|.
\fsign{genererClasses}{code\_cyclique \into classes\_latérales}{well ...}Génère les classes latérales associées au code spécifié. Parcours les vecteurs par poids croissant (d'abord ceux de poids 1, puis 2, etc…) et référence leur syndrome dans \verb|classes.rpz : vecteur -> vecteur| qui à un syndrome associe le représentant de la classe latérale de poids le plus faible.
\fsign{decoder2}{classes\_latérales \into vecteur \into vecteur}{n\cdot \ln(n)} Décode le mot $Z$ de $\FD^n$ donné. L'algorithme calcule le syndrome du mot, obtient le représentant de la classe latérale associée à ce vecteur $E$. Dans l'hypothèse où le mot reçu est effectivement décodable, alors, son «erreur» $E = Z-Y$, avec $Y$ le mot du code initialement envoyé, a la même classe latérale que $Z$. Donc $Y = Z+E$, on obtient un mot du code que l'on peut décoder.
\end{itemize}
\part*{Annexes}
\begin{figure}[h]
\begin{center}
\label{print_matriceExemple}
\includesvg[scale=.3]{print_output.svg}
\includesvg[scale=.3]{print_output_path.svg}
\caption{Exemple d'affichage de vecteur,matrice et polynômes}
\end{center}
\end{figure}

294
CompteRendu/print_output.svg
View File

@ -25,9 +25,9 @@
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="1.979899"
inkscape:cx="10.04794"
inkscape:cy="216.89603"
inkscape:zoom="0.35"
inkscape:cx="-109.9148"
inkscape:cy="-17.849234"
inkscape:document-units="mm"
inkscape:current-layer="layer1"
showgrid="false"
@ -48,7 +48,7 @@
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title />
<dc:title></dc:title>
</cc:Work>
</rdf:RDF>
</metadata>
@ -58,120 +58,178 @@
id="layer1"
transform="translate(-0.53453934,-1.3999026)">
<rect
style="opacity:1;fill:#686868;fill-opacity:1;stroke:none;stroke-width:1.76637125;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
style="opacity:1;fill:#686868;fill-opacity:1;stroke:none;stroke-width:3.70219326;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
id="rect827"
width="66.282837"
height="117.06406"
x="0.53453934"
y="1.3999026" />
<g
aria-label="┌011┐
│101│
│111│
│100│
└001┘"
style="font-style:normal;font-weight:normal;font-size:17.08358955px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="text12">
<path
d="m 12.454936,16.851757 h 5.980925 v 1.434754 h -4.646269 v 9.576153 h -1.334656 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path822" />
<path
d="m 23.399111,23.683524 q -2.001983,0 -3.011317,-1.634953 -1.017674,-1.643294 -1.017674,-4.821442 0,-3.18649 1.017674,-4.829785 1.009334,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800794 0.759085,2.001983 0.258589,1.192849 0.258589,2.827802 0,1.634953 -0.258589,2.827801 -0.25859,1.192848 -0.759085,1.993641 -1.026017,1.634953 -3.019658,1.634953 z m 0,-1.334655 q 1.192848,0 1.768418,-1.267923 0.57557,-1.267922 0.57557,-3.853817 0,-2.602578 -0.57557,-3.853818 -0.57557,-1.276264 -1.768418,-1.276264 -1.176165,0 -1.751735,1.267922 -0.291956,0.62562 -0.442105,1.576562 -0.141807,0.942601 -0.141807,2.285598 0,2.610919 0.583912,3.853817 0.583911,1.267923 1.751735,1.267923 z m 0.01668,-2.210523 q -0.25859,0 -0.408738,-0.358689 -0.150149,-0.358689 -0.250248,-0.842501 -0.08342,-0.392055 -0.141807,-0.925917 -0.05005,-0.542204 -0.05005,-0.825818 0,-0.200199 0.03337,-0.717378 0.03337,-0.517179 0.133465,-0.975966 0.241906,-1.192849 0.650645,-1.192849 0.233564,0 0.392055,0.316981 0.166832,0.316981 0.283614,0.900892 0.08342,0.408739 0.133465,0.925918 0.05005,0.517179 0.05005,0.809134 0,0.166832 -0.03337,0.658987 -0.02502,0.492154 -0.108441,1.009333 -0.20854,1.217873 -0.684011,1.217873 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path824" />
<path
d="m 30.789765,22.023547 h 2.619262 v -8.93385 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 v 11.035933 h 2.585895 v 1.418071 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path826" />
<path
d="m 41.066611,22.023547 h 2.619262 v -8.93385 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 v 11.035933 h 2.585895 v 1.418071 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path828" />
<path
d="m 53.562324,18.286511 h -4.637928 v -1.434754 h 5.972583 v 11.010907 h -1.334655 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path830" />
<path
d="m 12.454936,28.529992 h 1.334656 v 20.687159 h -1.334656 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path832" />
<path
d="m 20.512918,43.378034 h 2.619262 v -8.93385 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 v 11.035933 h 2.585895 v 1.418071 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path834" />
<path
d="m 33.675958,45.038011 q -2.001983,0 -3.011317,-1.634953 -1.017674,-1.643294 -1.017674,-4.821442 0,-3.18649 1.017674,-4.829785 1.009334,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800793 0.759085,2.001983 0.258589,1.192849 0.258589,2.827802 0,1.634952 -0.258589,2.827801 -0.25859,1.192848 -0.759085,1.993641 -1.026017,1.634953 -3.019658,1.634953 z m 0,-1.334655 q 1.192848,0 1.768418,-1.267923 0.57557,-1.267923 0.57557,-3.853817 0,-2.602579 -0.57557,-3.853818 -0.57557,-1.276264 -1.768418,-1.276264 -1.176165,0 -1.751736,1.267922 -0.291955,0.62562 -0.442104,1.576562 -0.141807,0.942601 -0.141807,2.285598 0,2.610919 0.583911,3.853817 0.583912,1.267923 1.751736,1.267923 z m 0.01668,-2.210523 q -0.25859,0 -0.408738,-0.358689 -0.150149,-0.358689 -0.250248,-0.842501 -0.08342,-0.392055 -0.141807,-0.925917 -0.05005,-0.542204 -0.05005,-0.825818 0,-0.200199 0.03337,-0.717378 0.03337,-0.517179 0.133466,-0.975967 0.241906,-1.192848 0.650644,-1.192848 0.233565,0 0.392055,0.316981 0.166832,0.316981 0.283615,0.900892 0.08342,0.408738 0.133465,0.925917 0.05005,0.517179 0.05005,0.809135 0,0.166832 -0.03337,0.658986 -0.02502,0.492155 -0.108441,1.009334 -0.20854,1.217873 -0.684011,1.217873 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path836" />
<path
d="m 41.066611,43.378034 h 2.619262 v -8.93385 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 v 11.035933 h 2.585895 v 1.418071 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path838" />
<path
d="m 53.562324,28.529992 h 1.334655 v 20.687159 h -1.334655 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path840" />
<path
d="m 12.454936,49.884479 h 1.334656 v 20.687159 h -1.334656 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path842" />
<path
d="m 20.512918,64.73252 h 2.619262 v -8.933849 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 V 64.73252 h 2.585895 v 1.418072 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path844" />
<path
d="m 30.789765,64.73252 h 2.619262 v -8.933849 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 V 64.73252 h 2.585895 v 1.418072 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path846" />
<path
d="m 41.066611,64.73252 h 2.619262 v -8.933849 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 V 64.73252 h 2.585895 v 1.418072 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path848" />
<path
d="m 53.562324,49.884479 h 1.334655 v 20.687159 h -1.334655 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path850" />
<path
d="m 12.454936,71.238966 h 1.334656 v 20.687159 h -1.334656 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path852" />
<path
d="m 20.512918,86.087007 h 2.619262 v -8.933849 l -1.9853,2.260572 -0.917576,-1.117774 2.886192,-3.244881 h 1.685003 v 11.035932 h 2.585895 v 1.418072 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path854" />
<path
d="m 33.675958,87.746985 q -2.001983,0 -3.011317,-1.634953 -1.017674,-1.643294 -1.017674,-4.821443 0,-3.186489 1.017674,-4.829784 1.009334,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800793 0.759085,2.001983 0.258589,1.192849 0.258589,2.827801 0,1.634953 -0.258589,2.827802 -0.25859,1.192848 -0.759085,1.993641 -1.026017,1.634953 -3.019658,1.634953 z m 0,-1.334655 q 1.192848,0 1.768418,-1.267923 0.57557,-1.267923 0.57557,-3.853818 0,-2.602578 -0.57557,-3.853817 -0.57557,-1.276264 -1.768418,-1.276264 -1.176165,0 -1.751736,1.267922 -0.291955,0.62562 -0.442104,1.576562 -0.141807,0.9426 -0.141807,2.285597 0,2.61092 0.583911,3.853818 0.583912,1.267923 1.751736,1.267923 z m 0.01668,-2.210523 q -0.25859,0 -0.408738,-0.358689 -0.150149,-0.358689 -0.250248,-0.842501 -0.08342,-0.392055 -0.141807,-0.925918 -0.05005,-0.542203 -0.05005,-0.825818 0,-0.200198 0.03337,-0.717377 0.03337,-0.517179 0.133466,-0.975967 0.241906,-1.192848 0.650644,-1.192848 0.233565,0 0.392055,0.316981 0.166832,0.31698 0.283615,0.900892 0.08342,0.408738 0.133465,0.925917 0.05005,0.517179 0.05005,0.809135 0,0.166832 -0.03337,0.658986 -0.02502,0.492155 -0.108441,1.009334 -0.20854,1.217873 -0.684011,1.217873 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path856" />
<path
d="m 43.952804,87.746985 q -2.001984,0 -3.011317,-1.634953 -1.017675,-1.643294 -1.017675,-4.821443 0,-3.186489 1.017675,-4.829784 1.009333,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800793 0.759085,2.001983 0.258589,1.192849 0.258589,2.827801 0,1.634953 -0.258589,2.827802 -0.25859,1.192848 -0.759085,1.993641 -1.026017,1.634953 -3.019658,1.634953 z m 0,-1.334655 q 1.192848,0 1.768418,-1.267923 0.57557,-1.267923 0.57557,-3.853818 0,-2.602578 -0.57557,-3.853817 -0.57557,-1.276264 -1.768418,-1.276264 -1.176166,0 -1.751736,1.267922 -0.291956,0.62562 -0.442104,1.576562 -0.141807,0.9426 -0.141807,2.285597 0,2.61092 0.583911,3.853818 0.583912,1.267923 1.751736,1.267923 z m 0.01668,-2.210523 q -0.25859,0 -0.408738,-0.358689 -0.150149,-0.358689 -0.250248,-0.842501 -0.08342,-0.392055 -0.141807,-0.925918 -0.05005,-0.542203 -0.05005,-0.825818 0,-0.200198 0.03337,-0.717377 0.03337,-0.517179 0.133466,-0.975967 0.241906,-1.192848 0.650644,-1.192848 0.233565,0 0.392055,0.316981 0.166832,0.31698 0.283615,0.900892 0.08342,0.408738 0.133465,0.925917 0.05005,0.517179 0.05005,0.809135 0,0.166832 -0.03337,0.658986 -0.02502,0.492155 -0.10844,1.009334 -0.20854,1.217873 -0.684011,1.217873 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path858" />
<path
d="m 53.562324,71.238966 h 1.334655 v 20.687159 h -1.334655 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path860" />
<path
d="m 12.454936,92.593453 h 1.334656 v 9.676247 h 4.646269 v 1.43476 h -5.980925 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path862" />
<path
d="m 23.399111,109.10147 q -2.001983,0 -3.011317,-1.63495 -1.017674,-1.6433 -1.017674,-4.82144 0,-3.186493 1.017674,-4.829788 1.009334,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800793 0.759085,2.001983 0.258589,1.192845 0.258589,2.827805 0,1.63495 -0.258589,2.8278 -0.25859,1.19285 -0.759085,1.99364 -1.026017,1.63495 -3.019658,1.63495 z m 0,-1.33465 q 1.192848,0 1.768418,-1.26793 0.57557,-1.26792 0.57557,-3.85381 0,-2.60258 -0.57557,-3.853821 -0.57557,-1.276264 -1.768418,-1.276264 -1.176165,0 -1.751735,1.267922 -0.291956,0.62562 -0.442105,1.576563 -0.141807,0.9426 -0.141807,2.2856 0,2.61092 0.583912,3.85381 0.583911,1.26793 1.751735,1.26793 z m 0.01668,-2.21053 q -0.25859,0 -0.408738,-0.35869 -0.150149,-0.35868 -0.250248,-0.8425 -0.08342,-0.39205 -0.141807,-0.92591 -0.05005,-0.54221 -0.05005,-0.82582 0,-0.2002 0.03337,-0.71738 0.03337,-0.51718 0.133465,-0.97597 0.241906,-1.192844 0.650645,-1.192844 0.233564,0 0.392055,0.316984 0.166832,0.31698 0.283614,0.90089 0.08342,0.40874 0.133465,0.92592 0.05005,0.51718 0.05005,0.80913 0,0.16683 -0.03337,0.65899 -0.02502,0.49215 -0.108441,1.00933 -0.20854,1.21787 -0.684011,1.21787 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path864" />
<path
d="m 33.675958,109.10147 q -2.001983,0 -3.011317,-1.63495 -1.017674,-1.6433 -1.017674,-4.82144 0,-3.186493 1.017674,-4.829788 1.009334,-1.634953 3.011317,-1.634953 2.001983,0 3.019658,1.634953 0.500495,0.800793 0.759085,2.001983 0.258589,1.192845 0.258589,2.827805 0,1.63495 -0.258589,2.8278 -0.25859,1.19285 -0.759085,1.99364 -1.026017,1.63495 -3.019658,1.63495 z m 0,-1.33465 q 1.192848,0 1.768418,-1.26793 0.57557,-1.26792 0.57557,-3.85381 0,-2.60258 -0.57557,-3.853821 -0.57557,-1.276264 -1.768418,-1.276264 -1.176165,0 -1.751736,1.267922 -0.291955,0.62562 -0.442104,1.576563 -0.141807,0.9426 -0.141807,2.2856 0,2.61092 0.583911,3.85381 0.583912,1.26793 1.751736,1.26793 z m 0.01668,-2.21053 q -0.25859,0 -0.408738,-0.35869 -0.150149,-0.35868 -0.250248,-0.8425 -0.08342,-0.39205 -0.141807,-0.92591 -0.05005,-0.54221 -0.05005,-0.82582 0,-0.2002 0.03337,-0.71738 0.03337,-0.51718 0.133466,-0.97597 0.241906,-1.192844 0.650644,-1.192844 0.233565,0 0.392055,0.316984 0.166832,0.31698 0.283615,0.90089 0.08342,0.40874 0.133465,0.92592 0.05005,0.51718 0.05005,0.80913 0,0.16683 -0.03337,0.65899 -0.02502,0.49215 -0.108441,1.00933 -0.20854,1.21787 -0.684011,1.21787 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path866" />
<path
d="m 41.066611,107.44149 h 2.619262 v -8.933845 l -1.9853,2.260575 -0.917576,-1.117777 2.886192,-3.244881 h 1.685003 v 11.035928 h 2.585895 v 1.41808 h -6.873476 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path868" />
<path
d="m 48.924396,102.2697 h 4.637928 v -9.676247 h 1.334655 v 11.111007 h -5.972583 z"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:Hack;-inkscape-font-specification:Hack;fill:#00f829;fill-opacity:1;stroke:none;stroke-width:0.42708972;stroke-opacity:1"
id="path870" />
</g>
width="256.40485"
height="132.93906"
x="-1.7333201"
y="-5.4036703" />
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:13.04045963px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.32601148"
x="2.3512421"
y="89.607773"
id="text841"><tspan
sodipodi:role="line"
id="tspan839"
x="2.3512421"
y="89.607773"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148">X^1 + X^2 + X^3</tspan><tspan
sodipodi:role="line"
x="2.3512421"
y="105.90835"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan843">1 + X^2</tspan><tspan
sodipodi:role="line"
x="2.3512421"
y="122.20892"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan845">1 + X^1 + X^4 + X^6 + X^9</tspan></text>
<flowRoot
xml:space="preserve"
id="flowRoot847"
style="fill:black;fill-opacity:1;stroke:none;font-family:sans-serif;font-style:normal;font-weight:normal;font-size:40px;line-height:1.25;letter-spacing:0px;word-spacing:0px"><flowRegion
id="flowRegion849"><rect
id="rect851"
width="137.14285"
height="50"
x="291.42856"
y="16.732544" /></flowRegion><flowPara
id="flowPara853"></flowPara></flowRoot> <text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:13.04045963px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.32601148"
x="151.86282"
y="13.561927"
id="text841-2"><tspan
sodipodi:role="line"
x="151.86282"
y="13.561927"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan845-9">┌011┐</tspan><tspan
sodipodi:role="line"
x="151.86282"
y="29.862503"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan883">│101│</tspan><tspan
sodipodi:role="line"
x="151.86282"
y="46.163078"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan885">│111│</tspan><tspan
sodipodi:role="line"
x="151.86282"
y="62.463654"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan887">│100│</tspan><tspan
sodipodi:role="line"
x="151.86282"
y="78.764229"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan889">└001┘</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:11.29124641px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.28228116"
x="222.2482"
y="9.1106415"
id="text841-2-7"><tspan
sodipodi:role="line"
x="222.2482"
y="9.1106415"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan889-0">┌1┐</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="23.224701"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan981">│1│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="37.338757"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan983">│0│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="51.452816"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan985">│1│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="65.566872"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan987">│0│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="79.680931"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan989">│0│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="93.794983"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan991">│1│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="107.90904"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan993">│1│</tspan><tspan
sodipodi:role="line"
x="222.2482"
y="122.02309"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12.21828365px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.28228116"
id="tspan995">└0┘</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:13.04045963px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.32601148"
x="8.7948952"
y="16.916115"
id="text841-2-6"><tspan
sodipodi:role="line"
x="8.7948952"
y="16.916115"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan889-2">┌100101110┐</tspan><tspan
sodipodi:role="line"
x="8.7948952"
y="33.21669"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan1011">│101011000│</tspan><tspan
sodipodi:role="line"
x="8.7948952"
y="49.517265"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan1013">│011000000│</tspan><tspan
sodipodi:role="line"
x="8.7948952"
y="65.817833"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:14.11111069px;line-height:1;font-family:Hack;-inkscape-font-specification:Hack;fill:#09ff26;fill-opacity:1;stroke-width:0.32601148"
id="tspan1015">└101011001┘</tspan></text>
<rect
style="opacity:1;fill:#09ff26;fill-opacity:1;stroke:none;stroke-width:1.14285779;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
id="rect1019"
width="146.68878"
height="1"
x="-1.7673719"
y="71.728836" />
<rect
style="opacity:1;fill:#09ff26;fill-opacity:1;stroke:none;stroke-width:1.1620723;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
id="rect1021"
width="75.831482"
height="1"
x="144.16548"
y="92.517525" />
<rect
style="opacity:1;fill:#09ff26;fill-opacity:1;stroke:none;stroke-width:1.19583499;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
id="rect1023"
width="1"
height="132.93539"
x="219.00478"
y="-5.4000192" />
<rect
style="opacity:1;fill:#09ff26;fill-opacity:1;stroke:none;stroke-width:1.80716944;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
id="rect1025"
width="1"
height="21.788689"
x="144.16548"
y="71.728836" />
</g>
</svg>

Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 18 KiB

After

Width:  |  Height:  |  Size: 12 KiB

10
Makefile
View File

@ -7,14 +7,12 @@ ascii: $(shell find textes/ -type f -iname "*.txt" ! -iname "*.ascii.txt" | sed
%.cmx: %.ml
ocamlopt -c $<
Code.cmo: Code.ml Math.cmo
Code.cmo: Code.ml Code.mli Math.cmo
ocamlc -c "Code.mli"
ocamlc -c "Code.ml"
%.cmi: %.mli
ocamlc -c $<
%.cmo: %.ml
if [ -f $*".mli" ]; then ocamlc -c $*".mli" ; fi
ocamlc -c $<
Math.cmo: Math.ml Math.mli
ocamlc -c Math.mli
ocamlc -c Math.ml
tipe: tipe.cmx
ocamlopt -o tipe str.cmxa tipe.cmx

43
Math.ml
View File

@ -130,11 +130,44 @@ let poldiveuc (p:polynome) (q:polynome) : (polynome * polynome) =
let poldiv (p:polynome) (q:polynome) : polynome = fst (poldiveuc p q);;
let polrst (p:polynome) (q:polynome) : polynome = snd (poldiveuc p q);;
(***************** Arbres de recherche de 'vecteurs' *****************)
type 'a binabr = BNoeud of 'a binabr * 'a binabr | BVal of 'a * 'a binabr | BFeuille;;
let isEmpty babr = babr=BFeuille;;(* Ne renvoie que les biens fondés, c'est à dire sans Noeud vide*)
exception NoSuchKeyException;;
let rec get ba (k:vecteur) =
match (ba,k) with
| (BNoeud(_,_) ,0)
| (BFeuille ,_) -> raise NoSuchKeyException
| (BVal(v,rr) ,0) -> v
| (BVal(v,rr) ,_) -> get rr k
| (BNoeud(t0,t1),_) ->
match k mod 2 with
| 0 -> get t0 (k lsr 1)
| 1 -> get t1 (k lsr 1)
| _ -> failwith "Félicitations, vous avez cassé les maths";;
let rec putWho ba (k:vecteur) v keepNew =
match (ba,k) with
| (BVal(old,rr) ,0) -> if keepNew then BVal(v,rr) else BVal(old,rr)
| (BFeuille ,0)
| (BNoeud(_,_) ,0) -> BVal(v,ba)
| (BVal(o,rr) ,_) -> BVal(o,putWho rr k v keepNew)
| (BFeuille ,_) -> putWho (BNoeud(BFeuille,BFeuille)) k v keepNew
(*match k mod 2 with
| 0 -> BNoeud(putWho BFeuille (k lsr 1) v keepNew, BFeuille)
| 1 -> BNoeud(BFeuille, putWho BFeuille (k lsr 1) v keepNew)
| _ -> failwith "Ich gratuliere Sie. Sie haben Mathe zerbrochen"
end*)
| (BNoeud(t0,t1),_) ->
match k mod 2 with
| 0 -> BNoeud(putWho t0 (k lsr 1) v keepNew, t1)
| 1 -> BNoeud(t0, putWho t1 (k lsr 1) v keepNew)
| _ -> failwith "99 7'4 c0mp1373m3n7 c4553 135 m47h5. 7u 73 23nd5 c0mp73 ?!";;
let put ba k v = putWho ba k v true;; (* Par défaut, on garde le nouveau *)

8
Math.mli
View File

@ -24,3 +24,11 @@ val polmul : polynome -> polynome -> polynome
val poldiveuc : polynome -> polynome -> polynome * polynome
val poldiv : polynome -> polynome -> polynome
val polrst : polynome -> polynome -> polynome
type 'a binabr = BNoeud of 'a binabr * 'a binabr | BVal of 'a * 'a binabr | BFeuille
exception NoSuchKeyException
val get : 'a binabr -> vecteur -> 'a
val putWho : 'a binabr -> vecteur -> 'a -> bool -> 'a binabr
val put : 'a binabr -> vecteur -> 'a -> 'a binabr

20
Test.ml
View File

@ -6,6 +6,24 @@ Sys.command "make Math.cmo Code.cmo";;
open Math;;
open Code;;
let print_boolean b = match b with
| true -> print_string "true"
| false -> print_string "false";;
let codeh = CLineaire.systematiqueFromRedondance 4 7 [7; 3; 5; 6];;
let vecteurs = matriceAuPif 9 (8-1);;
print_matrice 4 vecteurs;;
let classes = CLineaire.genererClasses codeh;;
let test v = try
CLineaire.encoder codeh (CLineaire.decoder codeh v) <> CLineaire.decoder2 classes v
with
Code.CLineaire.PasDansLeCodeException -> (print_int v;print_endline "*\n";false) in
List.find_opt test vecteurs;;
CLineaire.decoder codeh 119;;
CLineaire.encoder codeh 1;;
CLineaire.decoder2 classes 119;;
exit 0;;
(* Test du produit de matrice *)
let matest = [0b01110; 0b00101; 0b10111];;
print_matrice 5 matest;;
@ -78,7 +96,7 @@ print_matrice 4 cocylined.h;;
CLineaire.distance_minimale cocylined;;
print_vecteur 7 (cyclencode cocycl 0b1010);;
print_vecteur 9 203;;
(* Essayons de générer une table d'addition *)