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U.F.R.DESSCIENCESETDESTECHNIQUES UN
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ii2.1Denitionsetpremieresproprietes
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iv CODESETINTERPRETATIONS
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partagelebureaupendantdeuxans.Pourt
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viii engenetique[AM95].Lebutdelathe
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admettentchacuneuneversiondutheorem
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egala1:lescodesnon-interpretes. xii
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21.1Monodes ciativeetquipossedeunel
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4primitifsitousseselementssontprimi
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61.3.2Ensemblesrationnels Lafamille
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8Proposition1.4.3Unsous-monodeMAest
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10 codesadelaidedechirageborne,code
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12 jacentess'ilexistei2[0;n]etj2[0;
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14 CHAPITRE1.PRELIMINAIRES
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16 erreurdetransmissionappara^tdans
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18y1 CHAPITRE2.CODESADELAID'INTERPR
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delaid.CommeXestuncode,onax6=". 20
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22 Preuve.SoientYBetZAdeuxcodesadel
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24(ii)Ilexistei>0,j>1,2S(X),x1;:::;
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26 {Supposonsyju2S(xi).Posonsalorsv
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28 dem^eme,onpose Posons CHAPITRE2.
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deX+(d). deX(b)ouencorelemotcdestla
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adjacent.Parl'absurde,supposonsX\S(
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34 {Enfait,lescodes(1;2n),(2n;1)-li
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36 {Unautreexempleinteressantestcel
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plementaires: Exemple2.5.1Lecoderat
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40x1g(0)=1g(1)=2 CHAPITRE2.CODESADE
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42 (x1:::xf(q))12Xcequiimpliquerait
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44Leschema2.3reprendlesprincipauxre
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quisontinclusesdanslafamilledescode
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construction: centemaispasd'exhiber
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acelledec,parhypothesederecurrence,
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52Eneet,onaU1(X)=P(X)nf"g=fabab;abc
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ni: Theoreme3.2.2LabaseYdel'envelop
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56 CHAPITRE3.THEOREMEDUDEFAUTETCODE
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Proposition3.4.4UnmonodeNestextr^em
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pretee.SiunmotdeXadmetuneX-interpre
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qu'ilssontenfaitdescodesnon-interpr
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64 CHAPITRE3.THEOREMEDUDEFAUTETCODE
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maximaldanslafamilledescodes?Lefait
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Codesprexes,suxesetbixes Nouspresen
- Page 84 and 85: YFtelqueXYonaY=X.Evidemment,cetteno
- Page 86 and 87: mauxnishormisA,c'estenparticulierle
- Page 88 and 89: estuncodebixemaximal,nonmaximaldans
- Page 90 and 91: coupantestmentionneen[Per84]:fanbnj
- Page 92 and 93: 78 CHAPITRE4.SURLESCODESMAXIMAUX
- Page 94 and 95: 80 consisteamontrerque,pourtoutcode
- Page 96 and 97: 82 {Sinonilexisteunmotz2X00etdesmot
- Page 98 and 99: 84 s0 CHAPITRE5.MAXIMALITEETCOMPLET
- Page 100 and 101: 86 5.2Unemethodedecompletion d'alph
- Page 102 and 103: ni. uniformementsynchronisants(cf.T
- Page 104 and 105: 90 {jt0j
- Page 106 and 107: 92 {Sijsj>jt2jalorsilexistes02Atelq
- Page 108 and 109: 94t0).Soientz002Xetp2P(X)deuxmotste
- Page 110 and 111: 96c1 CHAPITRE5.MAXIMALITEETCOMPLETU
- Page 112 and 113: 98 Preuve.Nousallonsmontrerquepourt
- Page 114 and 115: veriantt1wt2=xt1r0t2y. 100contredit
- Page 116 and 117: 102 CHAPITRE5.MAXIMALITEETCOMPLETUD
- Page 118 and 119: t0=yxyxetV=(t0A\At0)nAt0Xt0AnAt0X+n
- Page 120 and 121: 106 CHAPITRE6.CODESSYNCHRONISANTSMA
- Page 122 and 123: possibilite. P(1:::k01yxyx)etdonck2
- Page 124 and 125: montrequek=k. 110Nousallonsmontrerq
- Page 126 and 127: 112Onajkjjkj
- Page 128 and 129: nisantmaximalY.DeplussiXestuncodera
- Page 130 and 131: uneintersectionnonvideaveclafamille
- Page 132 and 133: lelemmesuivant: preservelasuxitedel
- Page 136 and 137: lemme7.1.1assurequeby0n'estpasS-com
- Page 138 and 139: 124 V:l'ensembleVestsuxe. Nousavons
- Page 140 and 141: 126 (b)Ilestclairquelecasfz01;:::;z
- Page 142 and 143: 128Parconsequent,leseulcasquipeutap
- Page 144 and 145: doncn>m. P(x).Deplusonab(ab)n2P(x),
- Page 146 and 147: 132impliqueb:(ab)jvj:v:a2P(w:a),c'e
- Page 148 and 149: 134bad0bd1 as0 dibabCHAPITRE7.CODES
- Page 150 and 151: 136obtientdonc Ainsi,ona CommeUestb
- Page 152 and 153: maximalitedeUdansFcirc. 138 Lemme7.
- Page 154 and 155: 1.LRab(z)\Ujzj16=;. Extendab(z),cel
- Page 156 and 157: 142etu00=k+2:::h0:((ab)m0a)1,d'ouu0
- Page 158 and 159: 144 L'ensembleUestdoncmaximaldansFc
- Page 160 and 161: 146 Preuve.Consideronslasuitedes M(
- Page 162 and 163: 148 Onaalors: 9n02N;8y2X;8(s;p)2(y)
- Page 164 and 165: 1509n2N;8y2X;8(s;p)2(y)\(S(X)P(X))
- Page 166 and 167: 152 CODESETINTERPRETATIONS
- Page 168 and 169: 154 [Bru91a]V.Bruyere,Codes,Dissert
- Page 170 and 171: 156 [NC92]J.NeraudetM.Crochemore,As
- Page 172 and 173: 158 CODESETINTERPRETATIONS
- Page 174 and 175: 160prexe,8,68,75,122 rationnel,38,1
- Page 176 and 177: 162 INDEX
- Page 178 and 179: 164P(X) S(X) Ensembledesprexesnontr
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