Asymptotically good LCD 2-quasi-abelian codes over finite fields

In this paper, we construct a class of linear complementary dual (LCD for short) 2quasi-abelian codes over a finite field. Based on counting the number of such codes and estimating the number of the codes in this class whose relative minimum weights are small, we prove that the class of LCD 2-quasi-abelian codes over any finite field is asymptotically good. The existence of such codes is unconditional, which is different from the case of self-dual 2-quasi-abelian codes over a special finite field. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.