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

TL;DR

This paper introduces new methods using composite matrices from group rings to construct previously unknown binary self-dual codes of lengths 80, 84, and 96, enhancing coding theory knowledge.

Contribution

It presents novel techniques for constructing self-dual codes over finite rings, leading to the discovery of new binary self-dual codes of specific lengths.

Findings

Constructed best known singly-even binary self-dual codes of lengths 80, 84, 96

Developed new techniques using composite matrices from group rings

Discovered doubly-even binary self-dual codes of length 96 not previously known

Abstract

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 Frobenius rings. By applying these techniques over different alphabets, we construct best known singly-even binary self-dual codes of lengths 80, 84 and 96 as well as doubly-even binary self-dual codes of length 96 that were not known in the literature before.