Abstract
Let \(n=2(p^m-1)/(p-1)\), where p is an odd prime and \(m>1\) is a positive integer. In this paper, we research optimal p-ary constacyclic codes with two zeros. Two classes of optimal p-ary \([n,n-2m,4]\) constacyclic codes are presented by searching the solutions of certain congruence equations over \(\mathbb {F}_{p^m}\). Four explicit constructions of optimal constacyclic codes with such parameters are provided. The dual codes of a subclass of these constacyclic codes are also investigated.
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This work is supported by the National Natural Science Foundation of China under Grant Nos. 61972126, 62002093, U21A20428 and 12171134.
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Zhou, Y., Kai, X. & Sun, Z. Optimal constacyclic codes with minimum distance four. AAECC (2024). https://doi.org/10.1007/s00200-024-00648-4
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DOI: https://doi.org/10.1007/s00200-024-00648-4