@article{Si2023, 
author = {Xuesong Si and Chuanze Niu},
title = {On skew cyclic codes over        M          2        (            F              2        )},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24434-24445},
keywords = {skew cyclic code, finite chain ring, skew polynomial rings, Gray map},
url = {https://www.sciopen.com/article/10.3934/math.20231246},
doi = {10.3934/math.20231246},
abstract = {The algebraic structure of skew cyclic codes over        M          2      (             F        2  ), using the              F        4  -cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree    d  (  x  ) is a free code generated by    d  (  x  ). According to our findings, skew cyclic codes of odd and even lengths are cyclic and    2-quasi-cyclic over        M          2        (            F              2        ), respectively. We provide the self-dual skew condition of Hermitian dual codes of skew cyclic codes. The generator polynomials of Euclidean dual codes are obtained. Furthermore, a spanning set of a double skew cyclic code over        M          2        (            F              2        ) is considered in this paper.}
}