2024/08/26 by Huaning Liu, Liu, Huaning, Arne Winterhof +1 · 1 citation
Computer Science · Engineering · #Bayesian Methods and Mixture Models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2408.14330
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the most interesting case of safe prime powers q, Gómez and Winterhof showed that a subfamily of the family of Golomb Costas permutations of \1,2,…,q-2\ of size φ(q-1) has maximal cross-correlation of order of magnitude at most q1/2. In this paper we study a larger family of Golomb Costas permutations and prove a weaker bound on its maximal cross-correlation. Considering the whole family of Golomb Costas permutations we show that large cross-correlations are very rare. Finally, we collect several conditions for a small cross-correlation of two Costas permutations. Our main tools are the Weil bound and the Szemerédi-Trotter theorem for finite fields.