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Strongly regular graphs associated with ternary bent functions. (English) Zbl 1267.05300
Summary: We prove a new characterization of weakly regular ternary bent functions via partial difference sets. Partial difference sets are combinatorial objects corresponding to strongly regular graphs. Using known families of bent functions, we obtain in this way new families of strongly regular graphs, some of which were previously unknown. One of the families includes an example in [N. Hamada and T. Helleseth, J. Stat. Plann. Inference 56, No. 1, 129–146 (1996; Zbl 0873.05025)], which was considered to be sporadic; using our results, this strongly regular graph is now a member of an infinite family. Moreover, this paper contains a new proof that the Coulter-Matthews and ternary quadratic bent functions are weakly regular.

MSC:
05E30 Association schemes, strongly regular graphs
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
Software:
Magma
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