New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction

TL;DR

This paper introduces a novel bordered construction method using λ-circulant matrices to generate new binary self-dual codes of specific lengths, expanding the known code parameters.

Contribution

It presents a new bordered construction technique for self-dual codes over rings, enabling the creation of previously unknown binary self-dual codes of lengths 56, 62, 78, 92, and 94.

Findings

Constructed new binary self-dual codes with unique parameters

Identified codes with previously unknown weight enumerator parameters

Demonstrated the effectiveness of the bordered construction method

Abstract

In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring of characteristic 2. Moreover, using our bordered construction together with the well-known building-up and neighbour methods, we construct many binary self-dual codes of lengths 56, 62, 78, 92 and 94 with parameters in their weight enumerators that were not known in the literature before.