On the depth spectrum of repeated-root constacyclic codes over finite chain rings

Abstract Let R be a finite commutative chain ring and γ be a fixed generator of the maximal ideal of R . For any unit w in R , ( 1 + w γ ) -constacyclic codes over R as a generalization of negacyclic codes over Z 4 are a class of important linear codes. In this paper, based on algebraic structure, the generator polynomials of all torsion codes of ( 1 + w γ ) -constacyclic codes of any length over R are first given. Then, by using these torsion codes, we completely determine the depth spectrums of ( 1 + w γ ) -constacyclic codes over R of any length.

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