Optimal p-ary codes from one-weight and two-weight codes over View Full Text


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Article Info

DATE

2015-01-22

AUTHORS

Minjia Shi, Patrick Solé

ABSTRACT

This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C_{k_1 ,k_2 ,k_3 } $\end{document} over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}_p + v\mathbb{F}_p^* $\end{document} with type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p^{2k_1 } p^{k_2 } p^{k_3 } $\end{document}. The authors introduce a distance-preserving Gray map from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathbb{F}_p + v\mathbb{F}_p )^n $\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}_p^{2n} $\end{document}. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}_p + v\mathbb{F}_p $\end{document}, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}_p + v\mathbb{F}_p $\end{document}, which meet the Griesmer bound. More... »

PAGES

679-690

References to SciGraph publications

  • 2008-02-28. Ring geometries, two-weight codes, and strongly regular graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2007-01-01. Determining the Number of One-Weight Cyclic Codes When Length and Dimension Are Given in ARITHMETIC OF FINITE FIELDS
  • 2000. One-weight Z4-linear Codes in CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS
  • 2014-08-09. Optimal binary codes from one-lee weight codes and two-lee weight projective codes over ℤ4 in JOURNAL OF SYSTEMS SCIENCE AND COMPLEXITY
  • 1999-12. On Perfect Ternary Constant Weight Codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2006-10. Projective two-weight codes with small parameters and their corresponding graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1981-03. Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields in COMBINATORICA
  • 2007-02-23. New classes of 2-weight cyclic codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2012-04-11. Good p-ary quasic-cyclic codes from cyclic codes over in JOURNAL OF SYSTEMS SCIENCE AND COMPLEXITY
  • 1997-07. The Correspondence Between Projective Codes and 2-weight Codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11424-015-3265-3

    DOI

    http://dx.doi.org/10.1007/s11424-015-3265-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1044540504


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