2023/04/19 by Radel Ben-Av, Giora Dula, Ben-Av, Radel +5
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2304.09495
openalex publication_date 2023/04/19 · openalex created_date 2023/04/24 · openalex updated_date 2026/07/28
In this paper we describe an algorithm for generating all the possible PIW(m,n,k) - integer m× n Weighing matrices of weight k up to Hadamard equivalence. Our method is efficient on a personal computer for small size matrices, up to m≤ n=12, and k≤ 50. As a by product we also improved the nsoks \citeriel2006nsoks algorithm to find all possible representations of an integer k as a sum of n integer squares. We have implemented our algorithm in Sagemath and as an example we provide a complete classification for n=m=7 and k=25. Our list of IW(7,25) can serve as a step towards finding the open classical weighing matrix W(35,25).