On the Hulls of Group Codes
Year: 2025
Type: preprint
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 $G$.
Source: arXiv (Cornell University)
Authors: Deng, Xiheng, Ren, Yuan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910555162
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