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MDS symbol-pair repeated-root constacylic codes of prime power lengths over \(\mathbb {F}_{q}+ u\mathbb {F}_{q} + u^{2}\mathbb {F}_{q} \)

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Abstract

MDS symbol-pair codes forms an optimal class of symbol-pair codes for their best error-correction capability. \(\psi \)-constacyclic codes of length \(p^s\) over \(\mathfrak {R}=\mathbb {F}_{q}+ u\mathbb {F}_{q} + u^{2}\mathbb {F}_{q}\,\, (u^3=0)\), where \(q=p^m \), \(\psi \) is a nonzero element of \(\mathbb {F}_{q}\), are precisely the ideals of the ring \( {\mathfrak {R}[x]}/{\langle x^{p^s}-\psi \rangle } \) which is a local finite non chain ring with the non principal maximal ideal \(\langle u, x-\varphi \rangle \), where \( \varphi \in \mathbb {F}_{q} \) satisfying \( \psi =\varphi ^{p^s} \). In this paper, all MDS symbol-pair \(\psi \)-constacyclic codes of length \(p^s\) over \(\mathfrak {R}\) are established.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdallah, B.P. 1796, Fès-Atlas, Fès, Morocco

    Jamal Laaouine & Mohammed E. Charkani

  2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam

    Hai Q. Dinh

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 700000, Vietnam

    Hai Q. Dinh

  4. Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, 52000, Thailand

    Woraphon Yamaka

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  1. Jamal Laaouine
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  2. Hai Q. Dinh
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  3. Mohammed E. Charkani
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  4. Woraphon Yamaka
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Correspondence to Jamal Laaouine.

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Laaouine, J., Dinh, H.Q., Charkani, M.E. et al. MDS symbol-pair repeated-root constacylic codes of prime power lengths over \(\mathbb {F}_{q}+ u\mathbb {F}_{q} + u^{2}\mathbb {F}_{q} \). J. Appl. Math. Comput. 69, 219–250 (2023). https://doi.org/10.1007/s12190-022-01738-7

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