@article{Qi2024, 
author = {Wei Qi},
title = {The polycyclic codes over the finite field  Fq},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {29707-29717},
keywords = {polycyclic codes, idempotent generator, check matrix, MDS codes},
url = {https://www.sciopen.com/article/10.3934/math.20241439},
doi = {10.3934/math.20241439},
abstract = {This article extended the properties of the idempotent generator of cyclic codes to polycyclic codes over the finite field  Fq. In addition, the check matrix of polycyclic codes was provided over  Fq. Specifically, it has been proven that the constacyclic code is an  MDS code over  Fq if and only if its annihilator dual code is also an  MDS code. Finally, we have provided some examples of good codes.}
}