Consta-dihedral Codes over Finite Fields

03/01/2023

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by   Yun Fan, et al.

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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.