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A class of constacyclic codes over a finite field-II

Authors
  • Raka, Madhu1
  • 1 Panjab University, Centre for Advanced Study in Mathematics, Chandigarh, 160 014, India , Chandigarh (India)
Type
Published Article
Journal
Indian Journal of Pure and Applied Mathematics
Publisher
Indian National Science Academy
Publication Date
Sep 23, 2015
Volume
46
Issue
6
Pages
809–825
Identifiers
DOI: 10.1007/s13226-015-0158-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} be a finite field with q = pm elements, where p is any prime and m ≥ 1. In this paper, we explicitly determine all the μ-constacyclic codes of length ℓn over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document}, where ℓ is an odd prime coprime to p and the order of μ is a power of ℓ. All the repeated-root λ- constacyclic codes of length ℓnps over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} are also determined for any nonzero λ in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document}. As examples all the λ-constacyclic codes of length 3nps over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} for p = 5, 7, 11, 19 for n ≥ 1, s ≥ 1 are derived. We also obtain all the self-orthogonal negacyclic codes of length ℓn over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} when q is odd prime power and give some illustrative examples.

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