New record-breaking binary linear codes constructed from group codes

Abstract

In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to construct linear codes. Finally, we obtain some linear codes which have better parameters than the code in \cite{bib5}. All the calculation results and corresponding data are listed in the paper or posted online.

For now, this is the initial version which was completed in April 2024, and the authors will add some new results in the future