Few-weight ZpZp[u]-additive codes from down-sets View Full Text


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Article Info

DATE

2021-09-08

AUTHORS

Shukai Wang, Minjia Shi

ABSTRACT

In this paper, we study a special class of ZpZp[u]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_p{\mathbb {Z}}_p[u]$$\end{document}-additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document} defined in terms of the down-set, where u2=u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^2=u$$\end{document} and p is an odd prime. By a proper choice of the down-set, we determine the weight distribution of the additive code CL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_L$$\end{document}. In particular, we obtain several infinite families of minimal and optimal few-weight p-codes via the Gray map, and these codes can be applied to secret sharing schemes. More... »

PAGES

1-8

References to SciGraph publications

  • 2017-10-24. Few-weight codes from trace codes over a local ring in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2019-08-14. One-weight and two-weight ℤ2ℤ2[u,v]-additive codes in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2017-11-24. Linear codes from simplicial complexes in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2017-10-28. New Classes of p-Ary Few Weight Codes in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
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    http://dx.doi.org/10.1007/s12190-021-01594-x

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