Two generalizations on the minimum Hamming distance of repeated-root constacyclic codes

We study constacyclic codes, of length \(np^s\) and \(2np^s\), that are generated by the polynomials \((x^n + \gamma)^{\ell}\) and \((x^n - \xi)^i(x^n + \xi)^j\)\ respectively, where \(x^n + \gamma\), \(x^n - \xi\) and \(x^n + \xi\) are irreducible over the alphabet \(\F_{p^a}\). We generalize the r...

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Bibliographic Details
Published in:arXiv.org 2009-06
Main Authors: Ozadam, Hakan, Ozbudak, Ferruh
Format: Article
Language:English
Subjects:
Fields (mathematics)
Polynomials
Online Access:Get full text
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Summary:We study constacyclic codes, of length \(np^s\) and \(2np^s\), that are generated by the polynomials \((x^n + \gamma)^{\ell}\) and \((x^n - \xi)^i(x^n + \xi)^j\)\ respectively, where \(x^n + \gamma\), \(x^n - \xi\) and \(x^n + \xi\) are irreducible over the alphabet \(\F_{p^a}\). We generalize the results of [5], [6] and [7] by computing the minimum Hamming distance of these codes. As a particular case, we determine the minimum Hamming distance of cyclic and negacyclic codes, of length \(2p^s\), over a finite field of characteristic \(p\).
ISSN:2331-8422