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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;
- Page 28 and 29: 14 CHAPITRE1.PRELIMINAIRES
- Page 30 and 31: 16 erreurdetransmissionappara^tdans
- Page 32 and 33: 18y1 CHAPITRE2.CODESADELAID'INTERPR
- Page 34 and 35: delaid.CommeXestuncode,onax6=". 20
- Page 36 and 37: 22 Preuve.SoientYBetZAdeuxcodesadel
- Page 38 and 39: 24(ii)Ilexistei>0,j>1,2S(X),x1;:::;
- Page 40 and 41: 26 {Supposonsyju2S(xi).Posonsalorsv
- Page 42 and 43: 28 dem^eme,onpose Posons CHAPITRE2.
- Page 44 and 45: deX+(d). deX(b)ouencorelemotcdestla
- Page 46 and 47: adjacent.Parl'absurde,supposonsX\S(
- Page 48 and 49: 34 {Enfait,lescodes(1;2n),(2n;1)-li
- Page 50 and 51: 36 {Unautreexempleinteressantestcel
- Page 52 and 53: plementaires: Exemple2.5.1Lecoderat
- Page 54 and 55: 40x1g(0)=1g(1)=2 CHAPITRE2.CODESADE
- Page 56 and 57: 42 (x1:::xf(q))12Xcequiimpliquerait
- Page 58 and 59: 44Leschema2.3reprendlesprincipauxre
- Page 60 and 61: quisontinclusesdanslafamilledescode
- Page 62 and 63: construction: centemaispasd'exhiber
- Page 64 and 65: acelledec,parhypothesederecurrence,
- Page 66 and 67: 52Eneet,onaU1(X)=P(X)nf"g=fabab;abc
- Page 68 and 69: ni: Theoreme3.2.2LabaseYdel'envelop
- Page 70 and 71: 56 CHAPITRE3.THEOREMEDUDEFAUTETCODE
- Page 72 and 73: Proposition3.4.4UnmonodeNestextr^em
- Page 74 and 75: pretee.SiunmotdeXadmetuneX-interpre
- Page 76 and 77: qu'ilssontenfaitdescodesnon-interpr
- Page 80 and 81: maximaldanslafamilledescodes?Lefait
- Page 82 and 83: 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
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nisantmaximalY.DeplussiXestuncodera
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uneintersectionnonvideaveclafamille
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lelemmesuivant: preservelasuxitedel
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120{Supposonsx2Xety2U.Pardenitionde
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lemme7.1.1assurequeby0n'estpasS-com
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124 V:l'ensembleVestsuxe. Nousavons
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126 (b)Ilestclairquelecasfz01;:::;z
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128Parconsequent,leseulcasquipeutap
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doncn>m. P(x).Deplusonab(ab)n2P(x),
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132impliqueb:(ab)jvj:v:a2P(w:a),c'e
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134bad0bd1 as0 dibabCHAPITRE7.CODES
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136obtientdonc Ainsi,ona CommeUestb
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maximalitedeUdansFcirc. 138 Lemme7.
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1.LRab(z)\Ujzj16=;. Extendab(z),cel
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142etu00=k+2:::h0:((ab)m0a)1,d'ouu0
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144 L'ensembleUestdoncmaximaldansFc
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146 Preuve.Consideronslasuitedes M(
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148 Onaalors: 9n02N;8y2X;8(s;p)2(y)
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1509n2N;8y2X;8(s;p)2(y)\(S(X)P(X))
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152 CODESETINTERPRETATIONS
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154 [Bru91a]V.Bruyere,Codes,Dissert
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156 [NC92]J.NeraudetM.Crochemore,As
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158 CODESETINTERPRETATIONS
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160prexe,8,68,75,122 rationnel,38,1
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162 INDEX
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164P(X) S(X) Ensembledesprexesnontr
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