2025/04/22 by Farouk Adda, Adda, Farouk
Computer Science · #05C31 (Secondary) #15B20 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2504.15980
openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Butson matrices are square orthogonal matrices, denoted by BH(m,n), whose entries are the complex mth roots of unity and satisfy the condition BH(m,n)⋅BH(m,n)^*=nIn, where BH(m,n)^* is the conjugate transpose of BH(m,n) and In is the identity matrix. In this work, we propose constructions for BH(m,(n-1)n) then BH(m,((n)/(2)-1)n), when n and m are even numbers, using the existing BH(m,n). For each case, we provide two construction methods: one uses a single input Butson matrix, and another uses two input Butson matrices. Moreover, we present some results about the construction of Hadamard matrices.