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

22-02-2021 | Original Paper

A note on the construction and enumeration of Euclidean self-dual skew-cyclic codes

Authors: Irwansyah, Intan Muchtadi-Alamsyah, Ahmad Muchlis, Aleams Barra, Djoko Suprijanto

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

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Abstract

Let \(\theta \) be an automorphism on a finite field \(\mathbb {F}_q.\) In this paper, we give a way to construct and enumerate Euclidean self-dual \(\theta \)-cyclic codes of length n over \(\mathbb {F}_q\) when n is even and \(\gcd (n,|\theta |)=1.\) The restriction \(\gcd (n,|\theta |)=1\) implies that the \(\theta \)-cyclic codes are in fact cyclic codes and \(q=2^m,\) for some integer \(m\ge 1.\) The construction and enumeration are done by analyzing the orbits of cyclotomic cosets under a multiplier map induced by \(\theta .\)
previous article Peterson–Gorenstein–Zierler algorithm for differential convolutional codes
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Literature
1.
Jia, Y., Ling, S., Xing, C.: On self-dual cyclic codes over finite fields. IEEE Trans. Inf. Theory 57(4), 2243–2251 (2011)MathSciNetCrossRef
2.
3.
Boucher, D., Geiselmann, W., Ulmer, F.: Skew-cyclic codes. Appl. Algebra Eng. Commun. Comput. 18(4), 379–389 (2007)MathSciNetCrossRef
4.
Boucher, D.: A note on the existence of self-dual skew codes over finite fields. Lecture Notes in Computer Science, Proccedings in Honour of Thierry Berger 9084, 228–239 (2015)MathSciNetCrossRef
5.
Boucher, D., Ulmer, F.: Self-dual skew-codes and factorization of skew-polynomials. J. Symb. Comput. 60, 47–61 (2013)MathSciNetCrossRef
6.
Boucher, D.: Construction and number of self-dual skew codes over \({\mathbb{F}}_{p^{2}}\). Adv. Math. Commun. 10(4), 765–795 (2016)MathSciNetCrossRef
7.
Irwansyah, Barra, A., Muchtadi-Alamsyah, I., Muchlis, A., Suprijanto, D.: Skew-cyclic codes over \(B_k\). J. Appl. Math. Comput. 57(1–2), 69–84 (2018)MathSciNetCrossRef
8.
Siap, I., Abualrub, T., Aydin, N., Seneviratne, P.: Skew-cyclic codes of arbitrary length. Int. J. Inf. Coding Theory 2(1), 10–20 (2011)MathSciNetMATH
9.
Consorte, O.D., Valdez, L.D.: On Euclidean and Hermitian self-dual cyclic codes over \({\mathbb{F}}_{2^{r}}\). Philipp. J. Sci. (2016)
10.
11.
12.
Metadata
Title
A note on the construction and enumeration of Euclidean self-dual skew-cyclic codes
Authors
Irwansyah
Intan Muchtadi-Alamsyah
Ahmad Muchlis
Aleams Barra
Djoko Suprijanto
Publication date
22-02-2021
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/s00200-021-00495-7

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