Abstract
Let \({\mathfrak {R}}={\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\) with \(u^2=0\), where m, s are positive integers and p is an odd prime. For any invertible element \(\varLambda\) of \({\mathfrak {R}}\), the symbol-pair distances of all \(\varLambda\)-constacyclic codes of length \(2p^s\) over \({\mathfrak {R}}\) are completely obtained. We identify all symbol-pair Maximum Distance Separable (MDS) constacyclic codes of length \(2p^s\) over \({\mathfrak {R}}\). As examples, many new symbol-pair codes, as well as symbol-pair MDS codes are constructed.
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The authors are thankful for the research support from the INSPIRE Programme (INSPIRE Code-IF160375) of DST, Govt. Of India and IIT(ISM), Dhanbad, India.
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Dinh, H.Q., Singh, A.K. & Thakur, M.K. On symbol-pair distances of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\) and MDS symbol-pair codes. AAECC 34, 1027–1043 (2023). https://doi.org/10.1007/s00200-021-00534-3
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DOI: https://doi.org/10.1007/s00200-021-00534-3