Spread Codes from Abelian non-cyclic groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915126341271552 |
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| author | Climent, Joan-Josep Requena, Veronica Soler-Escrivà, Xaro |
| author_facet | Climent, Joan-Josep Requena, Veronica Soler-Escrivà, Xaro |
| contents | Given the finite field $\mathbb{F}_{q}$, for a prime power $q$, in this paper we present a way of constructing spreads of $\mathbb{F}_{q}^{n}$. They will arise as orbits under the action of an Abelian non-cyclic group. First, we construct a family of orbit codes of maximum distance using this group, and then we complete each of these codes to achieve a spread of the whole space having an orbital structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spread Codes from Abelian non-cyclic groups Climent, Joan-Josep Requena, Veronica Soler-Escrivà, Xaro Information Theory 11T71, 94B60, 20H30, 05E20, 68P30 Given the finite field $\mathbb{F}_{q}$, for a prime power $q$, in this paper we present a way of constructing spreads of $\mathbb{F}_{q}^{n}$. They will arise as orbits under the action of an Abelian non-cyclic group. First, we construct a family of orbit codes of maximum distance using this group, and then we complete each of these codes to achieve a spread of the whole space having an orbital structure. |
| title | Spread Codes from Abelian non-cyclic groups |
| topic | Information Theory 11T71, 94B60, 20H30, 05E20, 68P30 |
| url | https://arxiv.org/abs/2501.16838 |