Abstract
The real monomial representations of Clifford algebras give rise to two sequences of bent functions. For each of these sequences, the corresponding Cayley graphs are strongly regular graphs, and the corresponding sequences of strongly regular graph parameters coincide. Even so, the corresponding graphs in the two sequences are not isomorphic, except in the first 3 cases. The proof of this non-isomorphism is a simple consequence of a theorem of Radon.
Highlights
Two recent papers [10, 11] describe and investigate two infinite sequences of bent functions and their Cayley graphs
The bent function σm on Z22m is described in the first paper [10], on generalizations of Williamson’s construction for Hadamard matrices
The bent function τm on Z22m is described in the second paper [11], which investigates some of the properties of the two sequences of bent functions
Summary
Two recent papers [10, 11] describe and investigate two infinite sequences of bent functions and their Cayley graphs. The bent function τm on Z22m is described in the second paper [11], which investigates some of the properties of the two sequences of bent functions In this second paper it is shown that the bent functions σm and τm both correspond to Hadamard difference sets with the same parameters (vm, km, λm, nm) = (4m, 22m−1 − 2m−1, 22m−2 − 2m−1, 22m−2), and that their corresponding Cayley graphs are both strongly regular with the same parameters (vm, km, λm, λm). The main result of the current paper is the following.
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