Constacyclic Codes over Commutative Finite Principal Ideal Rings
Information Theory
2021-05-21 v1 math.IT
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2105.09547,
title = {Constacyclic Codes over Commutative Finite Principal Ideal Rings},
author = {Yun Fan},
journal= {arXiv preprint arXiv:2105.09547},
year = {2021}
}