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Published in: Applicable Algebra in Engineering, Communication and Computing 5/2022

20-11-2020 | Original Paper

Self-dual additive codes

Authors: Steven T. Dougherty, Adrian Korban, Serap Şahinkaya

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 5/2022

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Abstract

We define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. We determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes. We prove that there must exist self-dual codes under any duality for codes over a finite abelian group \({\mathbb {Z}}_{p^e}\). They exist for all lengths when p is prime and e is even; all even lengths when p is an odd prime with \(p \equiv 1 \pmod {4}\) and e is odd with \(e>1\); and all lengths that are \(0 \pmod {4}\) when p is an odd prime with \(p \equiv 3 \pmod {4}\) and e is odd with \(e>1.\)

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Metadata
Title
Self-dual additive codes
Authors
Steven T. Dougherty
Adrian Korban
Serap Şahinkaya
Publication date
20-11-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 5/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00473-5

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