Self-dual codes better than the Gilbert-Varshamov bound

被引：6

作者：

Bassa, Alp ^{[1
]}

Stichtenoth, Henning ^{[2
]}

机构：

[1] Bogazici Univ, Fac Arts & Sci, Dept Math, TR-34342 Istanbul, Turkey

[2] Sabanci Univ, MDBF, TR-34956 Istanbul, Turkey

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 01期

关键词：

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;

D O I：

10.1007/s10623-018-0497-y

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：173 / 182

页数：10

共 9 条

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