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Titolo:
Lower bounds on the state complexity of geometric Goppa codes
Autore:
Blackmore, T; Norton, GH;
Indirizzi:
Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia Univ QueenslandBrisbane Qld Australia 4072 Brisbane, Qld 4072, Australia
Titolo Testata:
DESIGNS CODES AND CRYPTOGRAPHY
fascicolo: 1, volume: 25, anno: 2002,
pagine: 95 - 115
SICI:
0925-1022(200201)25:1<95:LBOTSC>2.0.ZU;2-3
Fonte:
ISI
Lingua:
ENG
Soggetto:
GENERALIZED HAMMING WEIGHTS; HIERARCHY;
Keywords:
geometric Goppa codes; Hermitian codes; state complexity; gonality sequence; dimension/length profiles; Clifford's theorem;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Engineering, Computing & Technology
Citazioni:
13
Recensione:
Indirizzi per estratti:
Citazione:
T. Blackmore e G.H. Norton, "Lower bounds on the state complexity of geometric Goppa codes", DES CODES C, 25(1), 2002, pp. 95-115

Abstract

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or degG greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes. ) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one followsin a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

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Documento generato il 26/01/20 alle ore 09:51:31