Bassa, Alp and Stichtenoth, Henning (2019) Self-dual codes better than the Gilbert-Varshamov bound. Designs, Codes, and Cryptography, 87 (1). pp. 173-182. ISSN 0925-1022 (Print) 1573-7586 (Online)
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Official URL: http://dx.doi.org/10.1007/s10623-018-0497-y
Abstract
We show that every self-orthogonal code over Fq of length n can be extended to a self-dual code, if there exists self-dual codes of length n. Using a family of Galois towers of algebraic function fields we show that over any nonprime field Fq, with q64, except possibly q=125, there are infinite families of self-dual codes, which are asymptotically better than the asymptotic Gilbert-Varshamov bound.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Self-dual codes; Algebraic geometry codes; Gilbert-Varshamov Bound; Tsfasman-Vladut-Zink Bound; Towers of function fields; Asymptotically good codes; Quadratic forms; Witt's Theorem; 14G50; 94B27; 94B65; 15A63; 11T71 |
| Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
| Depositing User: | Henning Stichtenoth |
| Date Deposited: | 15 May 2020 16:28 |
| Last Modified: | 27 May 2023 20:20 |
| URI: | https://research.sabanciuniv.edu/id/eprint/37123 |
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