Turkish Journal of Mathematics
Abstract
In 1979, Miller proved that for a group $G$ of odd order, two minimal group codes in $\mathbb{F}_2G$ are $G$-equivalent if and only if they have identical weight distribution. In 2014, Ferraz-Guerreiro-Polcino Milies disproved Miller's result by giving an example of two non-$G$-equivalent minimal codes with identical weight distribution. In this paper, we give a characterization of finite abelian groups so that over a specific set of group codes, equality of important parameters of two codes implies the $G$-equivalence of these two codes. As a corollary, we prove that two minimal codes with the same weight distribution are $G$-equivalent if and only if for each prime divisor $p$ of $ G $, the Sylow $p$-subgroup of $G$ is homocyclic.
DOI
10.55730/1300-0098.3296
Keywords
Abelian group codes, weight distribution, $G$-equivalence, homocyclic group
First Page
2701
Last Page
2713
Recommended Citation
AKSU, F. A, & TUVAY, İ (2022). A characterization of abelian group codes in terms of their parameters. Turkish Journal of Mathematics 46 (7): 2701-2713. https://doi.org/10.55730/1300-0098.3296
