Galois LCD codes over mixed alphabets
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929605984649216 |
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| author | Bajalan, Maryam Fotue-Tabue, Alexandre Kabore, Joël Martínez-Moro, Edgar |
| author_facet | Bajalan, Maryam Fotue-Tabue, Alexandre Kabore, Joël Martínez-Moro, Edgar |
| contents | We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[θ]$-linear codes, where $p\in\{2; 3\}$ and $θ\neqθ^2=0$, that provides $\mathbb{F}_p$-linear complementary dual codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02843 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Galois LCD codes over mixed alphabets Bajalan, Maryam Fotue-Tabue, Alexandre Kabore, Joël Martínez-Moro, Edgar Information Theory We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[θ]$-linear codes, where $p\in\{2; 3\}$ and $θ\neqθ^2=0$, that provides $\mathbb{F}_p$-linear complementary dual codes. |
| title | Galois LCD codes over mixed alphabets |
| topic | Information Theory |
| url | https://arxiv.org/abs/2202.02843 |