Paul Leopardi


Australian National University

(professional staff, National Computational Infrastructure)

SCS Slide Set Classifying bent functions by their Cayley graphs


My investigation began with constructions for Hadamard matrices, as per the paper [1]. This resulted in a conjecture that an edge-coloured graph related to the Cayley graph of a bent function has an isomorphism that swaps the colours. I proved that two bent functions are involved, and presented this work at the ADTHM 2014 workshop in Lethbridge [2]. In later work I showed that the corresponding bent functions have isomorphic Cayley graphs only in the first 3 cases [3]. This led to deeper work on the Cayley graphs of bent functions as presented here and in the preprint [4].


[1] Paul Leopardi, "Constructions for Hadamard matrices, Clifford algebras, and their relation to amicability / anti-amicability graphs", Australasian Journal of Combinatorics, Volume 58(2) (2014), pp. 214–248. Preprint: Revised January 2014.

[2] Paul Leopardi, "Twin bent functions and Clifford algebras", in C. Colbourn (ed.) Algebraic Design Theory and Hadamard Matrices (ADTHM 2014), Springer, 2015, pp. 189-199. Preprint: arXiv:1501.05477 [math.CO].

[3] Paul Leopardi, "Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory", Journal of Algebra Combinatorics Discrete Structures and Applications, 4 (3) , 2017, pp. 271-280. Preprint: arXiv:1504.02827 [math.CO].

[4] Paul Leopardi, "Classifying bent functions by their Cayley graphs", Preprint: arXiv:1705.04507 [math.CO]. Revised, December, 2018.

See also