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Glasnik matematički, Vol. 58 No. 2, 2023.

Original scientific paper

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

Quasi-symmetric \(2\)-\((28,12,11)\) designs with an automorphism of order \(5\)

Renata Vlahović Kruc ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Vedran Krčadinac ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

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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.

Keywords

Quasi-symmetric design, automorphism group, orbit matrices

Hrčak ID:

312008

URI

https://hrcak.srce.hr/312008

Publication date:

23.12.2024.

Visits: 476 *

Publication date: 27 December 2023

Volume: Vol 58

Issue: Svezak 2

Pages: 159-166

DOI: 10.3336/gm.58.2.01

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Quasi-symmetric design, automorphism group, orbit matrices

Quasi-symmetric \(2\)-\((28,12,11)\) designs with an automorphism of order \(5\)

Renata Vlahović Kruc[1]

Email: renata.vlahovic.kruc@math.hr

Vedran Krčadinac[2]

Email: vedran.krcadinac@math.hr

 

[1] Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

[2] Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

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.

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