Linear complementary dual quasi-cyclic codes of index 2
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911387464237056 |
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| author | Abdukhalikov, Kanat Ho, Duy Ling, San Verma, Gyanendra K. |
| author_facet | Abdukhalikov, Kanat Ho, Duy Ling, San Verma, Gyanendra K. |
| contents | We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean, Hermitian, and symplectic inner products. As a consequence of these characterizations, we derive necessary and sufficient conditions for LCD one-generator quasi-cyclic codes. Furthermore, using these characterizations, we construct some new quasi-cyclic LCD codes over small fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear complementary dual quasi-cyclic codes of index 2 Abdukhalikov, Kanat Ho, Duy Ling, San Verma, Gyanendra K. Information Theory 94B05, 94B15, 94B60 We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean, Hermitian, and symplectic inner products. As a consequence of these characterizations, we derive necessary and sufficient conditions for LCD one-generator quasi-cyclic codes. Furthermore, using these characterizations, we construct some new quasi-cyclic LCD codes over small fields. |
| title | Linear complementary dual quasi-cyclic codes of index 2 |
| topic | Information Theory 94B05, 94B15, 94B60 |
| url | https://arxiv.org/abs/2504.09126 |