Optimal binary LCD codes

被引:0
作者
Stefka Bouyuklieva
机构
[1] St. Cyril and St. Methodius University,Faculty of Mathematics and Informatics
来源
Designs, Codes and Cryptography | 2021年 / 89卷
关键词
Optimal binary linear codes; LCD codes; 94B05; 94B65;
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学科分类号
摘要
Linear complementary dual codes (shortly LCD codes) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1992. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, cryptography, etc. In this paper, we prove some properties of binary LCD codes using their shortened and punctured codes. We also present some inequalities for the largest minimum weight dLCD(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{LCD}(n,k)$$\end{document} of binary LCD [n, k] codes for given length n and dimension k. Furthermore, we give two tables with the values of dLCD(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{LCD}(n,k)$$\end{document} for k≤32\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\le 32$$\end{document} and n≤40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\le 40$$\end{document}, and two tables with classification results.
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页码:2445 / 2461
页数:16
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