One-weight and two-weight ℤ2ℤ2[u,v]-additive codes View Full Text


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Article Info

DATE

2019-08-14

AUTHORS

Minjia Shi, Chenchen Wang, Rongsheng Wu, Yu Hu, Yaoqiang Chang

ABSTRACT

In this paper, a class of additive codes which is referred to as ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes is introduced. This is a generalization towards another direction of recently introduced ℤ2ℤ4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{4}$\end{document} codes (Doughterty et al., Appl. Algebra Eng. Commun. Comput. 27(2), 123–138, 7). A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, the structure and possible weights for all one-weight and two-weight ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes are described. Additionally, we also construct some one-weight and two-weight ℤ2ℤ2[u,v]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]$\end{document}-additive codes to illustrate our obtained results. More... »

PAGES

443-454

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
  • 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
  • 2009-06-17. Linear codes over in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2015-09-23. One weight Z2Z4 additive codes in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2015-01-22. Optimal p-ary codes from one-weight and two-weight codes over in JOURNAL OF SYSTEMS SCIENCE AND COMPLEXITY
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s12095-019-00391-5

    DOI

    http://dx.doi.org/10.1007/s12095-019-00391-5

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