Glasnik Matematicki, Vol. 58, No. 2 (2023), 159-166. \( \)

QUASI-SYMMETRIC \(2\)-\((28,12,11)\) DESIGNS WITH AN AUTOMORPHISM OF ORDER \(5\)

Renata Vlahović Kruc and Vedran Krčadinac

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail:renata.vlahovic.kruc@math.hr

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail:vedran.krcadinac@math.hr

Abstract.   A design is called quasi-symmetric if it has only two block intersection numbers. Using a method based on orbit matrices, we classify quasi-symmetric \(2\)-\((28,12,11)\) designs with intersection numbers \(4\), \(6\), and an automorphism of order \(5\). There are exactly \(31\,696\) such designs up to isomorphism.

2020 Mathematics Subject Classification.   05B05

Key words and phrases.   Quasi-symmetric design, automorphism group, orbit matrices

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.58.2.01

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