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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-08-13

AUTHORS

Liqin Qian, Minjia Shi, Patrick Solé

ABSTRACT

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. More... »

PAGES

717-734

References to SciGraph publications

  • 2017-07-20. On self-dual double circulant codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2016-09-27. Two and three weight codes over Fp+uFp in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2018-01-22. On self-dual negacirculant codes of index two and four in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2017-12-14. Statistical properties of side-channel and fault injection attacks using coding theory in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2003-08. On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2017-07-26. Some classes of quasi-twisted codes over finite chain rings in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
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    http://scigraph.springernature.com/pub.10.1007/s12095-018-0322-5

    DOI

    http://dx.doi.org/10.1007/s12095-018-0322-5

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