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One-weight codes in some classes of group rings
Applicable Algebra in Engineering, Communication and Computing ( IF 0.6 ) Pub Date : 2020-11-20 , DOI: 10.1007/s00200-020-00471-7
Raul Antonio Ferraz , Ruth Nascimento Ferreira

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:

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。
更新日期:2020-11-20
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