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.

中文翻译：

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某些类群环中的单权码

令 $${\mathbb {F}}_q$$ 是一个有 q 个元素的有限域，G 是一个有限阿贝尔群。在这项工作中，我们给出了条件，以确保在 G 是具有 n 个元素的循环群的情况下，$${\mathbb {F}}_qG$$ 中的代码是单权代码，使得 $${\text {gcd}}(n,q) = 1$$ ，并且当 G 是阿贝尔群时也是如此。