Publicação: CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON
Nenhuma Miniatura disponível
Data
2012-08-01
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
World Scientific Publ Co Pte Ltd
Tipo
Artigo
Direito de acesso
Acesso restrito
Resumo
It is very well known that algebraic structures have valuable applications in the theory of error-correcting codes. Blake [Codes over certain rings, Inform. and Control 20 (1972) 396-404] has constructed cyclic codes over Z(m) and in [Codes over integer residue rings, Inform. and Control 29 (1975), 295-300] derived parity check-matrices for these codes. In [Linear codes over finite rings, Tend. Math. Appl. Comput. 6(2) (2005) 207-217]. Andrade and Palazzo present a construction technique of cyclic, BCH, alternant, Goppa and Srivastava codes over a local finite ring B. However, in [Encoding through generalized polynomial codes, Comput. Appl. Math. 30(2) (2011) 1-18] and [Constructions of codes through semigroup ring B[X; 1/2(2) Z(0)] and encoding, Comput. Math. Appl. 62 (2011) 1645-1654], Shah et al. extend this technique of constructing linear codes over a finite local ring B via monoid rings B[X; 1/p(k) Z(0)], where p = 2 and k = 1, 2, respectively, instead of the polynomial ring B[X]. In this paper, we construct these codes through the monoid ring B[X; 1/kp Z(0)], where p = 2 and k = 1, 2, 3. Moreover, we also strengthen and generalize the results of [Encoding through generalized polynomial codes, Comput. Appl. Math. 30(2) (2011) 1-18] and [Constructions of codes through semigroup ring B[X; 1/2(2) Z(0)]] and [Encoding, Comput. Math. Appl. 62 (2011) 1645-1654] to the case of k = 3.
Descrição
Palavras-chave
Idioma
Inglês
Como citar
Journal of Algebra and Its Applications. Singapore: World Scientific Publ Co Pte Ltd, v. 11, n. 4, p. 19, 2012.
