Optimal binary codes from one-lee weight codes and two-lee weight projective codes over ℤ4 View Full Text


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Article Info

DATE

2014-08-09

AUTHORS

Minjia Shi, Yu Wang

ABSTRACT

This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over ℤ4. The authors first give the Pless identities on the Lee weight of linear codes over ℤ4. Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively, the construction methods of one-Lee weight and two-Lee weight projective codes over ℤ4 are also given. Finally, the authors recall the weight-preserving Gray map from (ℤ4n, Lee weight) 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}_2^{2n} $\end{document}, Hamming weight), and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes, which reach the Plotkin bound and the Griesmer bound. More... »

PAGES

795-810

References to SciGraph publications

  • 2008-02-28. Ring geometries, two-weight codes, and strongly regular graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2000. One-weight Z4-linear Codes in CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS
  • 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
  • 2007-02-23. New classes of 2-weight cyclic codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1997-07. The Correspondence Between Projective Codes and 2-weight Codes in DESIGNS, CODES AND CRYPTOGRAPHY
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    http://scigraph.springernature.com/pub.10.1007/s11424-014-2188-8

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    http://dx.doi.org/10.1007/s11424-014-2188-8

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