On transitive designs and strongly regular graphs constructed from Mathieu group M₁₁

2017/06/18 by Dean Crnković, Andrea Švob, Crnkovic, Dean +1
Computer Science · Engineering · Mathematics · #05B05 #05E18 #05E30 #20D06 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1706.05727

openalex publication_date 2017/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct structures from Mathieu group M₁₁. We classify transitive t-designs with 11, 12 and 22 points admitting a transitive action of Mathieu group M₁₁. Thereby we proved the existence of designs with parameters 3-(22,7,18) and found first simple designs with parameters 4-(11,5,6) and 5-(12,6,6). Additionally, we proved the existence of 2-designs with certain parameters having 55 and 66 points. Furthermore, we classified strongly regular graphs on at most 450 vertices admitting a transitive action of the Mathieu group M₁₁.

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