Linear complementary pairs of codes over a finite non-commutative Frobenius ring
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929395575291904 |
|---|---|
| author | Bhowmick, Sanjit Liu, Xiusheng |
| author_facet | Bhowmick, Sanjit Liu, Xiusheng |
| contents | In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes $(C,D)$ to be LCP of codes over finite non-commutative Frobenius rings. The minimum distances $d(C)$ and $d(D^\perp)$ are defined as the security parameter for an LCP of codes $(C, D).$ It was recently demonstrated that if $C$ and $D$ are both $2$-sided LCP of group codes over a finite commutative Frobenius rings, $D^\perp$ and $C$ are permutation equivalent in \cite{LL23}. As a result, the security parameter for a $2$-sided group LCP $(C, D)$ of codes is simply $d(C)$. Towards this, we deliver an elementary proof of the fact that for a linear complementary pair of codes $(C,D)$, where $C$ and $D$ are linear codes over finite non-commutative Frobenius rings, under certain conditions, the dual code $D^\perp$ is equivalent to $C.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear complementary pairs of codes over a finite non-commutative Frobenius ring Bhowmick, Sanjit Liu, Xiusheng Information Theory 51E22, 94B05 In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes $(C,D)$ to be LCP of codes over finite non-commutative Frobenius rings. The minimum distances $d(C)$ and $d(D^\perp)$ are defined as the security parameter for an LCP of codes $(C, D).$ It was recently demonstrated that if $C$ and $D$ are both $2$-sided LCP of group codes over a finite commutative Frobenius rings, $D^\perp$ and $C$ are permutation equivalent in \cite{LL23}. As a result, the security parameter for a $2$-sided group LCP $(C, D)$ of codes is simply $d(C)$. Towards this, we deliver an elementary proof of the fact that for a linear complementary pair of codes $(C,D)$, where $C$ and $D$ are linear codes over finite non-commutative Frobenius rings, under certain conditions, the dual code $D^\perp$ is equivalent to $C.$ |
| title | Linear complementary pairs of codes over a finite non-commutative Frobenius ring |
| topic | Information Theory 51E22, 94B05 |
| url | https://arxiv.org/abs/2406.15794 |