New binary self-dual codes via a generalization of the four circulant construction

TL;DR

This paper introduces a generalized four circulant construction method for self-dual codes, enabling the creation of new extremal binary self-dual codes of lengths 40, 64, and notably 68, with 43 new codes discovered.

Contribution

It extends the four circulant construction to new algebraic settings, leading to the discovery of numerous previously unknown extremal binary self-dual codes.

Findings

Constructed 43 new extremal binary self-dual codes of length 68.

Generated extremal codes of lengths 40 and 64.

Demonstrated the effectiveness of the generalized construction method.

Abstract

In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets F_2, F_2 + uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.