Constructions of codes through the semigroup ring [formula omitted] and encoding

Abstract

For any finite commutative ring B with an identity there is a strict inclusion B [ X ; Z 0 ] ⊂ B [ X ; 1 2 ; Z 0 ] ⊂ B [ X ; 1 2 2 Z 0 ] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B [ X ; 1 2 ; Z 0 ] . In this study we developed a construction technique of cyclic codes through a semigroup ring B [ X ; 1 2 2 Z 0 ] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B [ X ; 1 2 2 Z 0 ] . Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense.