A Note on Linear Codes over Semigroup Rings
DOI:
https://doi.org/10.5540/tema.2011.012.02.0079Abstract
Abstract. In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 13Z0] 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 tothe Hamming weight t r/2, i.e., whose minimum Hamming distance is r + 1.References
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