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Constacyclic Codes over Commutative Finite Principal Ideal Rings (2105.09547v1)
Published 20 May 2021 in cs.IT, math.IT, and math.RA
Abstract: For any constacyclic code over a finite commutative chain ring of length coprime to the characteristic of the ring, we construct explicitly generator polynomials and check polynomials, and exhibit a BCH bound for such constacyclic codes. As a consequence, such constacyclic codes are principal. Further, we get a necessary and sufficient condition that the cyclic codes over a finite commutative principal ideal ring are all principal. This condition is still sufficient for constacyclic codes over such rings being principal.