Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916767122587648 |
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| author | Marques, Adler Quoos, Luciane |
| author_facet | Marques, Adler Quoos, Luciane |
| contents | Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted significant interest. We construct infinite sequences $(C_i)_{i \geq 1}$ of LCD codes and of LCPs $(C', D')_{i \geq 1}$ over $\mathbb{F}_{q^2}$ obtained from the Garcia-Stichtenoth tower of function fields, where we describe suitable non-special divisors of small degree on each level of the tower. These families attain the Tsfasman-Vlăduţ-Zink bound and, for sufficiently large $q$ exceed the classic Gilbert-Varshamov bound, providing explicit asymptotically good constructions beyond existential results. We also exhibit infinite sequences of self-orthogonal over $\mathbb{F}_{q^2}$ and, when $q$ is even, self-dual codes from the same tower all meeting the Tsfasman-Vlăduţ-Zink bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound Marques, Adler Quoos, Luciane Algebraic Geometry Information Theory Primary 14G50, secondary 11T71, 94B27, 14Q05 Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted significant interest. We construct infinite sequences $(C_i)_{i \geq 1}$ of LCD codes and of LCPs $(C', D')_{i \geq 1}$ over $\mathbb{F}_{q^2}$ obtained from the Garcia-Stichtenoth tower of function fields, where we describe suitable non-special divisors of small degree on each level of the tower. These families attain the Tsfasman-Vlăduţ-Zink bound and, for sufficiently large $q$ exceed the classic Gilbert-Varshamov bound, providing explicit asymptotically good constructions beyond existential results. We also exhibit infinite sequences of self-orthogonal over $\mathbb{F}_{q^2}$ and, when $q$ is even, self-dual codes from the same tower all meeting the Tsfasman-Vlăduţ-Zink bound. |
| title | Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound |
| topic | Algebraic Geometry Information Theory Primary 14G50, secondary 11T71, 94B27, 14Q05 |
| url | https://arxiv.org/abs/2505.23937 |