Repeated-Root Constacyclic Codes Over the Chain Ring F p m [u]/⟨u 3 ⟩

Let Z = F_p^m[u]/(u³) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their dual codes. We also determine the number of codewords in each repeated-root constacyclic code over Z. We also obtain Hamming distances, RT distances, RT weight distributions and ranks (i.e., cardinalities of minimal generating sets) of some repeated-root constacyclic codes over Z. Using these results, we also identify some isodual and maximum distance separable (MDS) constacyclic codes over Z with respect to the Hamming and RT metrics.

Abstract licence: CC BY-NC-ND

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