Good p-ary quasic-cyclic codes from cyclic codes over View Full Text


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Article Info

DATE

2012-04-11

AUTHORS

Minjia Shi, Shanlin Yang, Shixin Zhu

ABSTRACT

This paper introduces a Gray map from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\mathbb{F}_p + v\mathbb{F}_p } \right)^n$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_p^{2n}$$\end{document}, and describes the relationship between codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_p + v\mathbb{F}_p$$\end{document} and their Gray images. The authors prove that every cyclic code of arbitrary length n over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_p + v\mathbb{F}_p$$\end{document} is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map. More... »

PAGES

375-384

References to SciGraph publications

  • 2006-01. Linear Codes over with Respect to the Rosenbloom–Tsfasman Metric in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2001-01. Codes over and Improvements to the Bounds on Ternary Linear Codes in DESIGNS, CODES AND CRYPTOGRAPHY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11424-012-0076-7

    DOI

    http://dx.doi.org/10.1007/s11424-012-0076-7

    DIMENSIONS

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