New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction

TL;DR

This paper introduces a new method for constructing binary self-dual codes using modified circulant matrices, resulting in previously unknown codes of specific lengths and weight enumerator parameters.

Contribution

It presents a novel construction technique for self-dual codes over Frobenius rings, leading to new codes of lengths 56, 58, 64, 80, and 92, including first-time examples with certain weight enumerators.

Findings

Constructed new self-dual codes of lengths 56, 58, 64, 80, and 92.

First known codes with specific weight enumerator parameters at length 80.

Demonstrated effectiveness of the modified four circulant construction.

Abstract

In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta\in\{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.