Sobre codigos hermitianos generalizados / On generalized hermitian codes
AUTOR(ES)
Alonso Sepulveda Castellanos
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), 46644669 (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 Bulygins. Next we list some of the results of our work with respect to GH-codes. We calculate true minimum distances, in particular, we improve Bulygins 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