Self-dual codes better than the Gilbert-Varshamov bound

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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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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