Abstract
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring. In this paper, the symbol-pair distances of all γ-constacyclic codes of length ps over R are completely determined.
Highlights
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Repeated-root constacyclic codes were first initiated in the most generality by Castagnoli in [10] and Van Lint in [11]
They established that the repeated-root constacyclic codes have a sequential structure, which motivated the researchers to further study these codes
Summary
Constacyclic codes are the pivotal and profound part of linear codes It includes as a subclass the important class of cyclic codes, which form the most important and well studied class of error-correcting codes. Repeated-root constacyclic codes were first initiated in the most generality by Castagnoli in [10] and Van Lint in [11] They established that the repeated-root constacyclic codes have a sequential structure, which motivated the researchers to further study these codes. The structure of and symbol-pair distance distibution of all constacyclic codes of length ps over F pm + uF pm were completely determined in [7,8,17].
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