Motivation

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].

References

[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 https://sites.google.com/site/paulleopardi/research

https://sites.google.com/site/paulleopardi/