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Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4)

Authors:	Dean Crnković BG Rodrigues Sanja Rukavina Vladimir D Tonchev

Institution:	1. Department of Mathematics, University of Rijeka, Radmile Matej?i? 2, 51000 Rijeka, Croatia;2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa;3. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA

Abstract:	This paper completes the enumeration of quasi-symmetric 2- $(64, 24, 46)$ designs supported by the dual code $C^{⊥}$ of the binary linear code $C$ spanned by the lines of $A G (3, 4)$ , initiated in Rodrigues and Tonchev (2015). It is shown that $C^{⊥}$ supports exactly 30,264 nonisomorphic quasi-symmetric 2- $(64, 24, 46)$ designs. The automorphism groups of the related strongly regular graphs are computed.

Keywords:	Quasi-symmetric design Linear code Automorphism group Strongly regular graph
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