A Note on Linear Codes over Semigroup Rings - Andrade, Antonio Aparecido de [UNESP]; Shah, Tariq; Khan, Atlas (Brazilian Society for Computational and Applied Mathematics (SBMAC), 2011)
In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.
Keywords: Semigroup ring; BCH code; Alternant code; Goppa code; Srivastava code