2012/08/26 by Liang Feng Zhang, Zhang, Liang Feng
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #cs.DM #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1208.5194
12 pages
openalex publication_date 2012/08/26 · arxiv created 2013/03/29 · arxiv updated 2013/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let m,n>1 be integers and ℙn,m be the point set of the projective (n-1)-space (defined by [2]) over the ring ℤmof integers modulo m. Let An,m=(auv) be the matrix with rows and columns being labeled by elements of ℙn,m, where auv=1 if the inner product < u,v >=0 and auv=0 otherwise. Let Bn,m=An,mAn,mt. The eigenvalues of Bn,m have been studied by [1, 2, 3], where their applications in the study of expanders and locally decodable codes were described. In this paper, we completely determine the eigenvalues of Bn,m for general integers m and n.