On the Hulls of Group Codes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908470943416320 |
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| author | Deng, Xiheng Ren, Yuan |
| author_facet | Deng, Xiheng Ren, Yuan |
| 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Hulls of Group Codes Deng, Xiheng Ren, Yuan Information Theory 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 $G$. |
| title | On the Hulls of Group Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2507.21623 |