Hermitian self-dual 2-quasi-abelian codes

作者：Zhang, Guanghui; Lin, Liren^*; Qin, Chunyan; Li, Ruibo

来源：Finite Fields and their Applications, 2024, 94: 102357.

DOI：10.1016/j.ffa.2023.102357

• Finite fields
• Quasi-abelian codes of index 2
• Asymptotically good
• Hermitian self-dual codes

In this paper, we construct a class of Hermitian self-dual 2-quasi-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 Hermitian self-dual 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 Euclidean self-dual 2-quasi-abelian codes over a special finite field.