Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions

TL;DR

This paper introduces three novel methods for constructing quaternary Hermitian self-dual codes using circulant matrices, leading to many new codes of specific lengths with improved properties.

Contribution

The paper presents three new techniques for constructing Hermitian self-dual codes over Frobenius rings, enhancing existing circulant methods and producing new codes of lengths 26, 32, 36, 38, and 40.

Findings

Constructed many new best known codes

Developed three new construction techniques

Extended the range of known code lengths

Abstract

In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using $\lambda$-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct many new best known quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40.