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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 3/2021

20-11-2020 | Original Paper

One-weight codes in some classes of group rings

Authors: Raul Antonio Ferraz, Ruth Nascimento Ferreira

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 3/2021

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Abstract

Let \({\mathbb {F}}_q\) be a finite field with q elements and G be a finite abelian group. In this work we gave conditions to ensure that a code in \({\mathbb {F}}_qG\) is a one-weight code in the case when G is a cyclic group with n elements, such that \({\text {gcd}}(n,q) = 1\), and also when G is an abelian group.
previous article Some remarks on n-absorbing subsemimodules
next article Left ideals of matrix rings and error-correcting codes

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Literature
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Chalom, G., Ferraz, R.A., Milies, C.Polcino: Essential idempotents and simplex codes. J. Algebra Comb. Discrete Struct. Appl. 4(2), 181–188 (2017)MathSciNetMATH
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Ferraz, R.A., Polcino Milies, C., Guerreiro, M.: G-equivalence in group algebras and minimal Abelian codes. IEEE Trans. Inf. Theory 60(1), 252–260 (2014)MathSciNetCrossRef
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Metadata
Title
One-weight codes in some classes of group rings
Authors
Raul Antonio Ferraz
Ruth Nascimento Ferreira
Publication date
20-11-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 3/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00471-7

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