On two-weight Z2k-codes View Full Text


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Article Info

DATE

2017-07-18

AUTHORS

Minjia Shi, Zahra Sepasdar, Adel Alahmadi, Patrick Solé

ABSTRACT

We determine the possible homogeneous weights of regular projective two-weight codes over Z2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_{2^k}$$\end{document} of length n>3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n>3$$\end{document}, with dual Krotov distance d◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d^{\lozenge }$$\end{document} at least four. The determination of the weights is based on parameter restrictions for strongly regular graphs applied to the coset graph of the dual code. When k=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=2$$\end{document}, we characterize the parameters of such codes as those of the inverse Gray images of Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document}-linear Hadamard codes, which have been characterized by their types by several authors. More... »

PAGES

1201-1209

References to SciGraph publications

  • 2008-02-28. Ring geometries, two-weight codes, and strongly regular graphs in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1975. The Association Schemes of Coding Theory in COMBINATORICS
  • 2001-06. Characterization of finite Frobenius rings in ARCHIV DER MATHEMATIK
  • 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
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    URI

    http://scigraph.springernature.com/pub.10.1007/s10623-017-0390-0

    DOI

    http://dx.doi.org/10.1007/s10623-017-0390-0

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