New record-breaking binary linear codes constructed from group codes

TL;DR

This paper introduces a novel method for constructing record-breaking binary linear codes using group rings and automorphism groups, resulting in codes with improved parameters over previous records.

Contribution

The paper presents a new construction approach for binary linear codes leveraging group rings and automorphism groups, achieving better code parameters than existing codes.

Findings

Constructed new binary linear codes with superior parameters

Utilized semidirect products of abelian and cyclic groups

Provided comprehensive data and calculations for the new 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.