One-weight codes in some classes of group rings

Abstract

Let $${\mathbb {F}}_q$$ be a finite field with q elements and G be a finite abelian group. In this work we gave conditions to ensure that a code in $${\mathbb {F}}_qG$$ is a one-weight code in the case when G is a cyclic group with n elements, such that $${\text {gcd}}(n,q) = 1$$ , and also when G is an abelian group.