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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.21623 |
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Table of Contents:
- 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 $G$.