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New self-dual codes of length 72

2017/05/16 by Alexandre Zhdanov, Zhdanov, Alexandre
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1705.05779

arxiv created 2017/05/16 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain at least 61 new singly even (Type I) binary [72,36,12] self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes) and at least 13 new doubly even (Type II) binary [72,36,12] self-dual codes by replacing the first row in each circulant in a double circulant code by "all ones" and "all zeros" vectors respectively.

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