Sobre codigos hermitianos generalizados / On generalized hermitian codes

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

We study Goppa codes (GH codes) based on certain algebraic function fields whose number of rational places is large. These codes generalize the well-known Hermitian codes; thus we might expect that they have good parameters. Bulygin (IEEE Trans. Inform. Theory 52 (10), 4664–4669 (2006)) initiate the study of GH-codes; while he considered only the even characteristic, our work is done regardless the characteristic. In any case our work was strongly influenced by Bulygin’s. Next we list some of the results of our work with respect to GH-codes. • We calculate “true minimum distances”, in particular, we improve Bulygin’s results; • We find bounds on the generalized Hamming weights, moreover, we show an algorithm to apply these computations to the cryptography; • We calculate an Automorphism subgroup; • We consider codes on certain subfields of the fields used for to construct GH-codes.

ASSUNTO(S)

codigos de goppa hermitian codes distancia minima minimum distance codigos hermitianos corpos de funções algebricas algebraic function fields goppa codes

Documentos Relacionados