New binary self-dual codes via a generalization of the four circulant\n construction

2019/12/25 by Joe Gildea, Gildea, Joe, Abidin Kaya +3
Computer Science · Engineering · Medicine · Social Sciences · #Cancer Mechanisms and Therapy #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Islamic Finance and Communication #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1912.11754

openalex publication_date 2019/12/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this work, we generalize the four circulant construction for self-dual\ncodes. By applying the constructions over the alphabets F₂, F₂ + uF₂,\nF₄+uF₄, we were able to obtain extremal binary self-dual codes of lengths 40,\n64 including new extremal binary self-dual codes of length 68. More precisely,\n43 new extremal binary self-dual codes of length 68, with rare new parameters\nhave been constructed.\n

Citations

• A new upper bound on the minimal distance of self-dual codes
• Shadow bounds for self-dual codes

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