On the Hulls of Group Codes

Xiheng Deng; Yuan Ren

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arXiv · 2507.21623

On the Hulls of Group Codes

Xiheng Deng·Yuan Ren

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Abstract

Let $\mathbb {F}_q$ be a finite field and $G$ a finte group with $(|G|,q)=1$. By a group code in $\mathbb {F}_q[G]$ we mean a two-sided ideal in $\mathbb {F}_q[G]$. We will prove a general criterion for the existence of group codes with given hull dimension, and then apply it to deduce explicit criterions for existence of group codes with hull dimension $\leq3$. In particular our criterion for the existence of $1$-dimensional hulls generalizes that of privious work which consider only abelian groups $G$.

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Xiheng Deng, Yuan Ren. 2025-07-29. On the Hulls of Group Codes. https://arxiv.org/abs/2507.21623

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