Double Circulant Self-Dual Codes From Generalized Cyclotomic Classes of Order Two

TL;DR

This paper introduces a novel method for constructing self-dual codes using generalized cyclotomic classes of order two, leading to new codes with high minimum weights over GF(2) and GF(4).

Contribution

It presents a new construction technique for double circulant self-dual codes based on generalized cyclotomy, achieving codes with optimal or near-optimal parameters.

Findings

Constructed self-dual codes with high minimum weights

Achieved codes over GF(2) and GF(4) with optimal parameters

Demonstrated the effectiveness of cyclotomic classes in code design

Abstract

In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over GF(2) and [32, 16, 8] almost optimal self-dual codes over GF(4). Based on the properties of generalized cyclotomy, some of these codes can be proved to possess good minimum weights.