$m$-adic residue codes over $\mathbb{F}_q[v]/(v^s-v)$.

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 $mathbb{F}_{q}[v]/(v^s-v).$ We determine the idempotent generators of the $m$-adic residue codes over $mathbb{F}_{q}[v]/(v^s-v)$. We obtain some parameters of optimal $m$-adic residue codes over $mathbb{F}_{q}[v]/(v^s-v),$ with respect to Griesmer bound for rings.