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Designs, Codes and Cryptography

Erschienen in:

31.03.2017

The primitive idempotents and weight distributions of irreducible constacyclic codes

verfasst von: Fengwei Li, Qin Yue

Erschienen in: Designs, Codes and Cryptography | Ausgabe 4/2018

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Abstract

Let \({\mathbb {F}}_q\) be a finite field with q elements such that \(l^v||(q^t-1)\) and \(\gcd (l,q(q-1))=1\), where l, t are primes and v is a positive integer. In this paper, we give all primitive idempotents in a ring \(\mathbb F_q[x]/\langle x^{l^m}-a\rangle \) for \(a\in {\mathbb {F}}_q^*\). Specially for \(t=2\), we give the weight distributions of all irreducible constacyclic codes and their dual codes of length \(l^m\) over \({\mathbb {F}}_q\).

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Titel: The primitive idempotents and weight distributions of irreducible constacyclic codes
verfasst von: Fengwei Li
Qin Yue
Publikationsdatum: 31.03.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 4/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0356-2

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