The full automorphism groups of the five symmetric (15,8,4)-designs

2025/06/20 by Mark Pankov, Pankov, Mark, Krzysztof Petelczyc +3
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Coding theory and cryptography #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2506.17216

Abstract

It is clear that the full automorphism group of the (15,8,4)-design of points and hyperplane complements of \rm PG(3,2) is \rm GL(4,2). Using methods of point-line geometries, we determine the full automorphism groups of the remaining four symmetric (15,8,4)-designs and describe their actions on the sets of points and blocks.

Citations

• Symmetric (15,8,4)-designs in terms of the geometry of binary simplex codes of dimension 4
• Point-line geometries related to binary equidistant codes
• A combinatorial proof of Fisher's Inequality

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