论文标题
阿贝尔组代码的特征在于其参数
A characterization of abelian group codes in terms of their parameters
论文作者
论文摘要
1979年，米勒（Miller）证明，对于$ \ mathbb {f} _2g $的两个最小组代码，$ g $ - 等于$ g $ - 如果它们具有相同的重量分布。 2014年，Ferraz-Guerreiro-Polcino Miles通过举例说明了两个非等效的最小代码，并反驳了米勒的结果，重量分布相同。在本文中，我们给出了有限的Abelian组的特征，以便在一组特定的组代码中，两个代码的重要参数的平等意味着这两个代码的$ G $等效性。作为推论，我们证明两个具有相同重量分布的最小代码是$ g $ - 等于$ g $当时，并且仅当每个Prime Divisor $ p $ $ | g | $，Sylow $ p $ -subgroup $ g $ of $ g $ is plyocyclic。
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 they have identical weight distribution. In 2014, Ferraz-Guerreiro-Polcino Milies disprove 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.
