English

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~FF with F=q{|F|=q} are asymptotically good if qq is even (odd respectively). In this paper, we investigate the algebraic property and the asymptotic property of conta-dihedral codes over FF, and show that: if qq is even or 4(q1)4\,|\,(q-1), 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}
}
R2 v1 2026-06-28T08:53:04.883Z