Negative Latin square type partial difference sets in nonabelian groups of order 64 |
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| Institution: | 1. Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany;2. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, Viale Lincoln, 5, I-81100 Caserta, Italy;1. Ruhr University Bochum, Universitätsstraße 150, 44801 Bochum, Germany;2. LAGA, University of Paris 8, Saint-Denis, France;3. Department of Informatics, University of Bergen, PB 7803, 5020 Bergen, Norway;4. Inria, 2 rue Simone Iff, 75012, Paris, France;1. Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon, Republic of Korea;2. Institute of Mathematical Sciences, Ewha Womans University, Seoul, Republic of Korea |
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| Abstract: | There exist few examples of negative Latin square type partial difference sets (NLST PDSs) in nonabelian groups. We present a list of 176 inequivalent NLST PDSs in 48 nonisomorphic, nonabelian groups of order 64. These NLST PDSs form 8 nonisomorphic strongly regular graphs. These PDSs were constructed using a combination of theoretical techniques and computer search, both of which are described. The search was run exhaustively on 212/267 nonisomorphic groups of order 64. |
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| Keywords: | Partial difference set Difference set Negative Latin square type |
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