The weight enumerators of singly-even self-dual [88, 44, 14] codes and new binary self-dual [68, 34, 12] and [88, 44, 14] codes

J Gildea, A Korban, AM Roberts - Finite Fields and Their Applications, 2024 - Elsevier
In this work, we focus on constructing binary self-dual [68, 34, 12] and [88, 44, 14] codes with
new parameters in their weight enumerators. For this purpose, we present a new bordered …

New binary self-dual codes of lengths 80, 84 and 96 from composite matrices

J Gildea, A Korban, AM Roberts - Designs, Codes and Cryptography, 2022 - Springer
In this work, we apply the idea of composite matrices arising from group rings to derive a
number of different techniques for constructing self-dual codes over finite commutative …

[HTML][HTML] A New Method for Constructing Self-Dual Codes over Finite Commutative Rings with Characteristic 2

Y Ma, J Nan, Y Liu - Mathematics, 2024 - mdpi.com
In this work, we present a new method for constructing self-dual codes over finite
commutative rings R with characteristic 2. Our method involves searching for k× 2 k matrices …

Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

J Gildea, A Korban, AM Roberts… - arXiv preprint arXiv …, 2021 - arxiv.org
In this work, we define a modification of a bordered construction for self-dual codes which
utilises $\lambda $-circulant matrices. We provide the necessary conditions for the …

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

AM Roberts - Applicable Algebra in Engineering, Communication …, 2022 - Springer
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 λ-circulant …

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

J Gildea, A Korban, AM Roberts - Finite Fields and Their Applications, 2021 - Elsevier
In this work, we give a new technique for constructing self-dual codes over commutative
Frobenius rings using λ-circulant matrices. The new construction was derived as a …

Group Codes, Composite Group Codes and Constructions of Self-Dual Codes

A Korban - 2021 - chesterrep.openrepository.com
The main research presented in this thesis is around constructing binary self-dual codes
using group rings together with some well-known code construction methods and the study …

Group rings: Units and their applications in self-dual codes

R Taylor - 2021 - chesterrep.openrepository.com
The initial research presented in this thesis is the structure of the unit group of the group ring
Cn x D6 over a field of characteristic 3 in terms of cyclic groups, specifically U (F3t (Cn x …