Abstract
In this paper, the structure of \((\alpha u+\beta (u-\delta ))\)-constacyclic codes of length n over the finite commutative non-local ring \(\frac{{\mathbb {F}}_{p^m}[u]}{\left\langle u^2-\delta u \right\rangle }\) is provided, where \(\alpha , \beta \) and \(\delta \) are units of \({\mathbb {F}}_{p^m}\). The structure of dual constacyclic codes is considered and the hull of all such codes is determined. Using that, the Hamming and symbol-pair distances of \((\alpha u+\beta (u-\delta ))\)-constacyclic code over the ring \(\frac{{\mathbb {F}}_{p^m}[u]}{\left\langle u^2-\delta u \right\rangle }\) are established for code length \(p^s\). As applications, the MDS and MDS symbol-pair codes among them are completely identified.
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The authors’ name are in alphabetical order. This paper is a part of Ph.D. thesis of Sampurna Satpati.
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Dinh, H.Q., Satpati, S. & Singh, A.K. Construction of optimal codes from a class of constacyclic codes. J. Appl. Math. Comput. 68, 3961–3977 (2022). https://doi.org/10.1007/s12190-021-01695-7
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DOI: https://doi.org/10.1007/s12190-021-01695-7