On self-dual and LCD quasi-twisted codes of index two over a special chain ring

被引:0
作者
Liqin Qian
Minjia Shi
Patrick Solé
机构
[1] Anhui University,Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education
[2] Anhui University,School of Mathematical Sciences
[3] CNRS/LAGA,undefined
来源
Cryptography and Communications | 2019年 / 11卷
关键词
Double circulant codes; Gray map; Self-dual codes; LCD codes; Quasi-twisted codes; 94 B15; 94 B25; 05 E30;
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中图分类号
学科分类号
摘要
Let q be a prime power, and let 𝔽q\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} denote the finite field of order q. Consider the chain ring Rk=𝔽q[u]/〈uk〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{k}=\mathbb {F}_{q}[u]/\langle u^{k}\rangle $\end{document} with k ≥ 1 an integer. We study self-dual and LCD quasi-twisted codes of index two and twisting constant λ over Rk for the metric induced by the standard Gray map. Some special factorizations of xm − λ over Rk are studied. By random coding, we obtain four classes of asymptotically good self-dual λ-circulant codes and four classes of asymptotically good LCD λ-circulant codes over Rk.
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页码:717 / 734
页数:17
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