2023/03/01 by Fan, Yun, Leng, Yue
#12E20 #13M10 #20C05 #94B60 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2303.00235
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~F with |F|=q are asymptotically good if q is even (odd respectively). In this paper, we investigate the algebraic property and the asymptotic property of conta-dihedral codes over F, and show that: if q is 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.