Original scientific paper

New binary self-dual codes via a variation of the four-circulant construction

Joe Gildea ; Department of Mathematics, University of Chester, UK
Abidin Kaya ; Department of Engineering Fundamentals, Faculty of Engineering and Technology, Sampoerna University, Indonesia
Bahattin Yildiz ; Department of Mathematics and Statistics, Northern Arizona University, USA

Abstract

In this work, we generalize the four circulant construction for self-dual
codes. By applying the constructions over the alphabets F_2, F_2+uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68.
More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.

Keywords

circulant matrices; extremal self-dual codes; Gray maps; extension theorems; neighboring construction

Hrčak ID:

244261

URI

https://hrcak.srce.hr/244261

Publication date:

29.9.2020.

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