Strongly regular graphs associated with ternary bent functions

Authors:
Yin Tan;Alexander Pott;Tao Feng
Affiliations:
School of Mathematical Sciences, Peking University, 100871 Beijing, China;Department of Mathematics, Otto-von-Guericke-University, 39106 Magdeburg, Germany;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

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Abstract

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, T. Helleseth, A characterization of some {3v"2+v"3,3v"1+v"2,3,3}-minihypers and some [15,4,9;3]-codes with B"2=0, J. Statist. Plann. Inference 56 (1996) 129-146], 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.