Consta-dihedral Codes over Finite Fields
Information Theory
2023-03-02 v1 math.IT
Abstract
It is proved in a reference (Fan, Lin, IEEE TIT, vol.67, pp.5016-5025) that the self-dual (LCD respectively) dihedral codes over a finite field~ with are asymptotically good if is even (odd respectively). In this paper, we investigate the algebraic property and the asymptotic property of conta-dihedral codes over , and show that: if is even or , then the self-dual consta-dihedral codes are asymptotically good; otherwise, the LCD consta-dihedral codes are asymptotically good. And, with the help of a technique developed in this paper, some errors in the reference mentioned above are corrected.
Cite
@article{arxiv.2303.00235,
title = {Consta-dihedral Codes over Finite Fields},
author = {Yun Fan and Yue Leng},
journal= {arXiv preprint arXiv:2303.00235},
year = {2023}
}