CYCLIC CODES THROUGH $B[X;\frac{a}{b}{\mathbb Z}_{0}]$, WITH $\frac{a}{b}\in {\mathbb Q}^{+}$ AND b = a+1, AND ENCODING

Abstract

Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and [Formula: see text] is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, Goppa codes, Srivastava codes through monoid ring [Formula: see text]. For a = 1, almost all the results contained in [16] stands as a very particular case of this study.