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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.12340 |
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| _version_ | 1866913782268166144 |
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| author | Caruso, Xavier Drain, Fabrice |
| author_facet | Caruso, Xavier Drain, Fabrice |
| contents | Given a finite extension $K/F$ of degree $r$ of a finite field $F$, we enumerate all selfdual skew cyclic codes in the Ore quotient ring $K[X;\text{Frob}]/(X^{rk}-1)$ for any positive integer $k$ coprime to the characteristic $p$ (separable case). We also provide an enumeration algorithm when $k$ is a power of $p$ (purely inseparable case), at the cost of some redundancies. Our approach is based on an explicit bijection between skew cyclic codes, on the one hand, and certain families of $F$-linear subspaces of some extensions of $K$. Finally, we report on an implementation in SageMath. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Selfdual skew cyclic codes Caruso, Xavier Drain, Fabrice Information Theory Given a finite extension $K/F$ of degree $r$ of a finite field $F$, we enumerate all selfdual skew cyclic codes in the Ore quotient ring $K[X;\text{Frob}]/(X^{rk}-1)$ for any positive integer $k$ coprime to the characteristic $p$ (separable case). We also provide an enumeration algorithm when $k$ is a power of $p$ (purely inseparable case), at the cost of some redundancies. Our approach is based on an explicit bijection between skew cyclic codes, on the one hand, and certain families of $F$-linear subspaces of some extensions of $K$. Finally, we report on an implementation in SageMath. |
| title | Selfdual skew cyclic codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.12340 |