Abstract
Let \(\mathcal {R}=\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m}, u^2=0 \), be the finite commutative chain ring with unity, where p is a prime number, m is a positive integer and \(\mathbb {F}_{p^m}\) is the finite field with \(p^m\) elements. In this work, we give a simple and short proof of classification of all \( \gamma \)-constacyclic codes of length \(p^s\) over \(\mathcal {R}\), that is, ideals of the ring \(\mathcal {R}[x]/\langle x^{p^{s}}- \gamma \rangle \), where \( \gamma \) is a nonzero element of the field \(\mathbb {F}_{p^m}\). This allows us to study the Hamming and symbol-pair distance distributions of all such codes.
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The authors would like to thank the reviewers and the editor for their valuable comments and suggestions, which have greatly improved the quality of this paper.
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Laaouine, J. (2020). 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: Belkasmi, M., Ben-Othman, J., Li, C., Essaaidi, M. (eds) Advanced Communication Systems and Information Security. ACOSIS 2019. Communications in Computer and Information Science, vol 1264. Springer, Cham. https://doi.org/10.1007/978-3-030-61143-9_12
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DOI: https://doi.org/10.1007/978-3-030-61143-9_12
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