m-adic residue codes over F_q[v]/(v^s-v)

10/28/2018

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by   Ferhat Kuruz, et al.

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Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The m-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the m-adic residue codes over the quotient ring F_q[v]/(v^s-v). We determine the idempotent generators of the m-adic residue codes over F_q[v]/(v^s-v). We obtain some parameters of optimal m-adic residue codes over F_q[v]/(v^s-v), with respect to Griesmer bound for rings.