Consta-Dihedral Codes and Their Asymptotic Properties
Yun Fan, Yue Leng · IEEE Transactions on Information Theory · 2025
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 fieldFwith$|F|=q$are asymptotically good ifqis even (odd respectively). In this paper, we investigate the algebraic structures and the asymptotic properties of consta-dihedral codes overF, and show that: ifqis even or$4\,|\,(q-1)$, 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.