CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON


Autoria(s): Shah, Tariq; De Andrade, Antonio Aparecido
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

20/05/2014

20/05/2014

01/08/2012

Resumo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 07/56052-8

Processo FAPESP: 11/03441-3

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.

Formato

19

Identificador

http://dx.doi.org/10.1142/S0219498812500788

Journal of Algebra and Its Applications. Singapore: World Scientific Publ Co Pte Ltd, v. 11, n. 4, p. 19, 2012.

0219-4988

http://hdl.handle.net/11449/22138

10.1142/S0219498812500788

WOS:000307044900016

Idioma(s)

eng

Publicador

World Scientific Publ Co Pte Ltd

Relação

Journal of Algebra and Its Applications

Direitos

closedAccess

Palavras-Chave #Semigroup ring #Cyclic code #BCH code #Alternant code #Goppa code #Srivastava code
Tipo

info:eu-repo/semantics/article