Balanced Weighing Matrices

2021/08/28 by Hadi Kharaghani, Kharaghani, Hadi, Thomas Pender +3
Engineering · #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2108.12593

openalex publication_date 2021/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A unified approach to the construction of weighing matrices and certain symmetric designs is presented. Assuming the weight p in a weighing matrix W(n,p) is a prime power, it is shown that there is a W(\fracp^m+1-1p-1(n-1)+1,p^m+1) for each positive integer m. The case of n=p+1 reduces to the balanced weighing matrices with classical parameters W(\fracp^m+2-1p-1,p^m+1). The equivalence with certain classes of association schemes is discussed in details.

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