2019/03/23 by Tai Duc, Duc, Tai Do
Engineering · Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1903.09824
openalex publication_date 2019/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group and let h be a positive integer. A BH(G,h) matrix is a G-invariant |G|× |G| matrix H whose entries are complex hth roots of unity such that HH^*=|G|I|G|, where H^* denotes the complex conjugate transpose of H, and I|G| is the identity matrix of order |G|. In this paper, we give three new constructions of BH(G,h) matrices. The first construction is the first known family of BH(G,h) matrices in which G does not need to be abelian. The second and the third constructions are two families of BH(G,h) matrices in which G is a finite local ring.