Constructions of \(t\)-designs from weighing matrices and association schemes
Year: 2026
Type: article
Abstract: We provide a method to construct \(t\)-designs from weighing matrices and association schemes. One instance of our method can produce a \(3\)-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to a question of Gunderson and Semeraro JCTB 2017. We explore variations of our method on some matrices that satisfy certain combinatorial restrictions. In particular, we show that there exist various infinite families of partially balanced incomplete block designs with block size four on the binary Hamming schemes and the \(3\)-class association schemes attached to symmetric designs, and regular pairwise balanced designs with block sizes three and four. Mathematics Subject Classifications: 05B05, 05C50, 05E30 Keywords: \(t\)-design, characteristic polynomial, weighing matrix, Hadamard matrix, association scheme
Source: Combinatorial Theory
DOI: 10.5070/c6.68661
Authors: Gary Greaves, Sho Suda
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4392271278