| Texto completo | |
| Autor(es): |
Cardell, Sara D.
;
Climent, Joan-Josep
;
Panario, Daniel
;
Stevens, Brett
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Advances in Mathematics of Communications; v. 14, n. 3, p. 17-pg., 2020-08-01. |
| Resumo | |
In this paper we construct F-2-linear codes over F-2(b) with length n and dimension n - r where n = rb. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime p, let n = p - 1 and utilize a partition of Z(n). Then we apply a Zech logarithm to the elements of these sets and use the results to construct an index array which represents the parity-check matrix of the code. These codes are always cyclic and the density of the parity-check and the generator matrices decreases to 0 as n grows (for a fixed r). When r = 2 we prove that these codes are always maximum distance separable. For higher r some of them retain this property. (AU) | |
| Processo FAPESP: | 16/50476-0 - Efficiency and security of pre and post quantum cryptographic methods: theory and applications |
| Beneficiário: | Ricardo Dahab |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |