We study the relationship between homogeneous bent functions and some intersection graphs of a special type that are called Nagy graphs and denoted by Γ(n,k). The graph Γ(n,k) is the graph whose vertices correspond to (nk) unordered subsets of size k of the set 1,.., n. Two vertices of Γ(n,k) are joined by an edge whenever the corresponding k-sets have exactly one common element. Those n and k for which the cliques of size k + 1 are maximal in Γ(n,k) are identified. We obtain a formula for the number of cliques of size k + 1 in Γ(n,k) for n = (k + 1)k/2. We prove that homogeneous Boolean functions of 10 and 28 variables obtained by taking the complement to the cliques of maximal size in Γ(10,4) and Γ(28,7) respectively are not bent functions.
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА
- 2.03 МЕХАНИКА И МАШИНОСТРОЕНИЕ