Double Circulant Self-dual Codes on Sextic Cyclotomy
Tongjiang Yan, Tao Wang, Wenpeng Gao, Xvbo Zhao
TL;DR
This paper introduces a new method for constructing self-dual codes using sextic cyclotomy, resulting in codes that are optimal or superior over GF(2) and GF(4).
Contribution
It presents novel constructions of double circulant self-dual codes based on sextic cyclotomic classes, expanding the coding theory toolkit.
Findings
Some codes are optimal self-dual codes.
Some codes outperform existing codes.
Codes are self-dual under certain conditions.
Abstract
This paper contributes to construct double circulant self-dual codes by sextic cyclotomy. Generator matrixes of a family of pure double circulant codes and a family of double circulant codes with boundary are formed from sextic cyclotomic classes. These codes are proved to be self-dual on certain conditions. Moreover, experiments show that some of them are optimal self-dual codes or best than ever codes over GF}(2) and GF}(4).
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Taxonomy
TopicsCoding theory and cryptography · Cancer Mechanisms and Therapy · Islamic Finance and Communication