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12 jacentess'ilexistei2[0;n]etj2[0;m]telsque DeuxX-interpretationsquinesontpasadjacentessontditesdisjointes. DeuxX-interpretations(s;d1;:::;dn;p)et(s0;d01;:::;d0m;p0)dumotwsontad- sd1:::di=s0d01:::d0j: CHAPITRE1.PRELIMINAIRES UneX-interpretation(";d1;:::;dn;")estditetriviale. UneX-interpretation(s;d1;:::;dn;p)telleques;p2Xestditequasi-triviale. uneX-interpretationpourl'occurrence(u;w0;v)dew0s'ilexistes2AX,p2 uneX-interpretationdew.LaX-interpretationI=(d0;d1;:::;dn;dn+1)induit XAeti;j2N,0
Proposition1.6.1SoitXuncodecirculairenietw2XunmottelquejwjX> lg(X).AlorstouteX-interpretationdewestadjacenteal'interpretationtriviale. 1.6.FACTORISATIONSETINTERPRETATIONS 13
Page 1: U.F.R.DESSCIENCESETDESTECHNIQUES UN
Page 4 and 5: ii2.1Denitionsetpremieresproprietes
Page 6 and 7: iv CODESETINTERPRETATIONS
Page 8 and 9: partagelebureaupendantdeuxans.Pourt
Page 10 and 11: viii engenetique[AM95].Lebutdelathe
Page 12 and 13: admettentchacuneuneversiondutheorem
Page 14 and 15: egala1:lescodesnon-interpretes. xii
Page 16 and 17: 21.1Monodes ciativeetquipossedeunel
Page 18 and 19: 4primitifsitousseselementssontprimi
Page 20 and 21: 61.3.2Ensemblesrationnels Lafamille
Page 22 and 23: 8Proposition1.4.3Unsous-monodeMAest
Page 24 and 25: 10 codesadelaidedechirageborne,code
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 78 and 79:
64 CHAPITRE3.THEOREMEDUDEFAUTETCODE
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
Page 128 and 129:
nisantmaximalY.DeplussiXestuncodera
Page 130 and 131:
uneintersectionnonvideaveclafamille
Page 132 and 133:
lelemmesuivant: preservelasuxitedel
Page 134 and 135:
120{Supposonsx2Xety2U.Pardenitionde
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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