Double skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916242571395072 |
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| author | Singh, Ashutosh Yildirim, Tulay Prakash, Om |
| author_facet | Singh, Ashutosh Yildirim, Tulay Prakash, Om |
| contents | In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets, generator matrices, and the dual codes over the ring $\mathrm{R}$. As an implementation, the obtained results are illustrated with some good examples. Moreover, we introduce a construction for new generator matrices and thus achieve codes with improved parameters compared to those found in existing literature. Finally, we tabulate our obtained block codes over the ring $\mathrm{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Double skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$ Singh, Ashutosh Yildirim, Tulay Prakash, Om Information Theory 94B05, 94B15 In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets, generator matrices, and the dual codes over the ring $\mathrm{R}$. As an implementation, the obtained results are illustrated with some good examples. Moreover, we introduce a construction for new generator matrices and thus achieve codes with improved parameters compared to those found in existing literature. Finally, we tabulate our obtained block codes over the ring $\mathrm{R}$. |
| title | Double skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$ |
| topic | Information Theory 94B05, 94B15 |
| url | https://arxiv.org/abs/2403.16833 |