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Published in: Applicable Algebra in Engineering, Communication and Computing 2/2023

01-02-2021 | Original Paper

A note on “H. Q. Dinh et al., Hamming distance of repeated-root constacyclic codes of length \(2p^{s}\) over \({\mathbb{F}}_{p^{m}}+ u{\mathbb{F}}_{p^{m}}\)

Authors: Jamal Laaouine, Mohammed Elhassani Charkani

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 2/2023

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Abstract

Let \({\mathcal{R}}\) be the finite chain ring \({\mathcal{R}}={\mathbb{F}}_{p^{m}}+ u{\mathbb{F}}_{p^{m}}(u^{2} = 0)\), where p is an odd prime number and m is a positive integer. For \(\eta \in {\mathbb{F}}_{p^{m}}^{*}\), the Hamming distances of all \(\eta\)-constacyclic codes of length \(2p^{s}\) over \({\mathcal{R}}\) had already been studied in Dinh et al. (in AAECC, 2020. https://​doi.​org/​10.​1007/​s00200-020-00432-0). However, such a study is incomplete. In this paper, we provide corrections to some results that appeared in Dinh et al. (2020) and we completely solve the problem of determination of the Hamming distance of \(\eta\)-constacyclic codes of length \(2p^{s}\) over \({\mathcal{R}}\).

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Literature
1.
go back to reference Chen, B., Dinh, H.Q., Liu, H., Wang, L.: Constacyclic codes of length \(2p^{s}\) over \({{\mathbb{F}}}_{p^{m}}+ u {{\mathbb{F}}}_{p^{m}}\). J. Finite Fields Appl. 37(Issue Issue C), 108–130 (2016)CrossRefMATH Chen, B., Dinh, H.Q., Liu, H., Wang, L.: Constacyclic codes of length \(2p^{s}\) over \({{\mathbb{F}}}_{p^{m}}+ u {{\mathbb{F}}}_{p^{m}}\). J. Finite Fields Appl. 37(Issue Issue C), 108–130 (2016)CrossRefMATH
3.
go back to reference Dinh, H.Q., Nguyen, B.T., Singh, A.K., Sriboonchitta, S.: Hamming and symbol pair distances of repeated root constacycliccodes of prime power lengths over \({\mathbb{F}}_{p^m}+ u {\mathbb{F}}_{p^m}\). IEEE Trans. Inf. Theory 64(4), 24174–2430 (2018)CrossRef Dinh, H.Q., Nguyen, B.T., Singh, A.K., Sriboonchitta, S.: Hamming and symbol pair distances of repeated root constacycliccodes of prime power lengths over \({\mathbb{F}}_{p^m}+ u {\mathbb{F}}_{p^m}\). IEEE Trans. Inf. Theory 64(4), 24174–2430 (2018)CrossRef
4.
go back to reference Laaouine, J.: On the Hamming and symbol-pair distance of constacyclic codes of length \(p^s\) over \({{\mathbb{F}}}_{p^m}+ u{{\mathbb{F}}}_{p^m}\). In: International Conference on Advanced Communication Systems and Information Security, pp. 137–154. Springer, Cham (2019) Laaouine, J.: On the Hamming and symbol-pair distance of constacyclic codes of length \(p^s\) over \({{\mathbb{F}}}_{p^m}+ u{{\mathbb{F}}}_{p^m}\). In: International Conference on Advanced Communication Systems and Information Security, pp. 137–154. Springer, Cham (2019)
5.
go back to reference Lopez-Permouth, S.R., Ozadam, H., Ozbudak, F., Szabo, S.: Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes. Finite Fields Appl. 19, 164–38 (2013)MathSciNetCrossRefMATH Lopez-Permouth, S.R., Ozadam, H., Ozbudak, F., Szabo, S.: Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes. Finite Fields Appl. 19, 164–38 (2013)MathSciNetCrossRefMATH
Metadata
Title
A note on “H. Q. Dinh et al., Hamming distance of repeated-root constacyclic codes of length over ”
Authors
Jamal Laaouine
Mohammed Elhassani Charkani
Publication date
01-02-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00492-w

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