Artigo
CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON
Fecha
2012-08-01Registro en:
Journal of Algebra and Its Applications. Singapore: World Scientific Publ Co Pte Ltd, v. 11, n. 4, p. 19, 2012.
0219-4988
10.1142/S0219498812500788
WOS:000307044900016
8940498347481982
Autor
Quaid I Azam Univ
Universidade Estadual Paulista (Unesp)
Resumen
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.