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

Author(s)

Shah, Tariq ^[1] ; De Andrade, Antonio Aparecido ^[2]

Affiliation

^[1] Quaid I Azam Univ, Dept Math, Islamabad - Pakistan

^[2] Sao Paulo State Univ, Dept Math, Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 11, n. 4 AUG 2012.
• Web of Science Citations: 4

Abstract

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. (AU)