Symmetric (15,8, 4)-designs in terms of the geometry of binary simplex codes of dimension 4

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外文摘要：Let n = 2~k - 1 and m = 2~(k-2) for a certain k ≥ 3. Consider the point-line geometry of 2m-element subsets of an n-element set. Maximal singular subspaces of this geometry correspond to binary simplex codes of dimension k. For k ≥ 4 the associated collinearity graph contains maximal cliques different from maximal singular subspaces. We investigate maximal cliques corresponding to symmetric (n, 2m, m)-designs. The main results concern the case k = 4 and give a geometric interpretation of the five well-known symmetric (15, 8,4)-designs.

外文关键词：

Point-line geometryCollinearity graphSimplex codeSymmetric design

作者：

Mark Pankov、Krzysztof Petelczyc、Mariusz Zynel

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作者单位：

Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Sloneczna 54, 10-710 Olsztyn, Poland

Faculty of Mathematics, University of Bialystok, Ciolkowskiego 1M, 15-245 Bialystok, Poland

出版年：

2025

DOI：

10.1007/s10623-025-01570-7

Designs, codes and cryptography

ISSN：0925-1022

年,卷(期)：2025.93(6)