On circulant self-dual codes over small fields

被引:0
作者
Markus Grassl
T. Aaron Gulliver
机构
[1] Universtität Karlsruhe (TH),Institut für Algorithmen und Kognitive Systeme (IAKS), Fakultät für Informatik
[2] Austrian Academy of Sciences,Institute for Quantum Optics and Quantum Information (IQOQI)
[3] University of Victoria,Department of Electrical and Computer Engineering
来源
Designs, Codes and Cryptography | 2009年 / 52卷
关键词
Self-dual codes; Circulant codes; Bounds on codes; 94B05; 94B65; 94B60;
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摘要
We construct self-dual codes over small fields \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}_q}$$\end{document} with q = 3, 4, 5, 7, 8, 9 of moderate length with long cycles in the automorphism group. With few exceptions, the codes achieve or improve the known lower bounds on the minimum distance of self-dual codes.
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