2023/10/13 by Manuel Albrizzio, Albrizzio, Manuel
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2310.10682
openalex publication_date 2023/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the action on \mathbbF2n by cyclic permutations (ℤ/nℤ). Two elements x, y∈ \mathbbF2n are in the same orbit if they are cyclic shifts of each other. Cryptographic properties of rotation symmetric Boolean functions can be efficiently computed using the square matrix nA, the construction of which uses orbit representatives of the cyclic shifting action. In 2018, Ciungu and Iovanov proved that nA2=2n⋅ I, the identity matrix of dimension gn× gn where gn is the number of orbits. In this paper, we answer the open question of the precise number of positive and negative eigenvalues of nA.