Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3296
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.
Keywords
Abelian group codes, weight distribution, $G$-equivalence, homocyclic group
First Page
2701
Last Page
2713
Recommended Citation
AKSU, FATMA ALTUNBULAK and TUVAY, İPEK
(2022)
"A characterization of abelian group codes in terms of their parameters,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 10.
https://doi.org/10.55730/1300-0098.3296
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/10
