2025/11/14 by Domonkos Czifra, Máté Matolcsi, Czifra, Domonkos +3
Engineering · Mathematics · #05B20 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2511.11230
openalex publication_date 2025/11/14 · openalex created_date 2025/11/18 · openalex updated_date 2026/07/28
Based on the concept of positive definite functions on finite groups, we present a new necessary condition for the existence of Butson Hadamard matrices BH(n,q). We use this condition to prove some nonexistence results for a sequence of values of (n,q), and also to facilitate a computer search and discover a matrix BH(18,14). Furthermore, we use cyclotomic cosets to construct matrices BH(34,10), BH(62,6), BH(82,6), and BH(146,6) for the first time. These matrices have a 2-circulant structure.