2018/07/01 by Constanza Riera, Patrick Solé, Riera, Constanza +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #14-3-3 protein interactions #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1807.00344
openalex publication_date 2018/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find a complete characterization of plateaued Boolean\nfunctions in terms of the associated Cayley graphs. Precisely, we show that a\nBoolean function f is s-plateaued (of weight =2(n+s-2)/2) if and only\nif the associated Cayley graph is a complete bipartite graph between the\nsupport of f and its complement (hence the graph is strongly regular of\nparameters e=0,d=2(n+s-2)/2). Moreover, a Boolean function f is\ns-plateaued (of weight \≠ 2(n+s-2)/2) if and only if the associated\nCayley graph is strongly 3-walk-regular (and also strongly\n\ℓ-walk-regular, for all odd \ℓ\≥ 3) with some explicitly given\nparameters.\n