Generalized bent Boolean functions and strongly regular Cayley graphs

2018/06/20 by Riera, Constanza, Stanica, Pantelimon, Gangopadhyay, Sugata
#05E30 #06E30 #94C10 #94C15 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1806.07601

Abstract

In this paper we define the (edge-weighted) Cayley graph associated to a generalized Boolean function, introduce a notion of strong regularity and give several of its properties. We show some connections between this concept and generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard spectrum. In particular, we find a complete characterization of quartic gbent functions in terms of the strong regularity of their associated Cayley graph.

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