Two and three weight codes over Fp+uFp View Full Text


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Article Info

DATE

2016-09-27

AUTHORS

Minjia Shi, Rongsheng Wu, Yan Liu, Patrick Solé

ABSTRACT

We construct an infinite family of three-Lee-weight codes of dimension 2m, where m is singly-even, over the ring Fp+uFp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{p}+u\mathbb {F}_{p}$\end{document} with u2=0. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain an infinite family of abelian p-ary three-weight codes. When m is odd, and p≡3 (mod 4), we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. An application to secret sharing schemes is given. More... »

PAGES

637-646

References to SciGraph publications

  • 2003-06-18. Covering and Secret Sharing with Linear Codes in DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
  • 2001-10. Duadic Codes over F2 + uF2 in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
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    http://scigraph.springernature.com/pub.10.1007/s12095-016-0206-5

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    http://dx.doi.org/10.1007/s12095-016-0206-5

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