Abstract
We examine the structure of weighing matricesW(n, w), wherew=n−2,n−3,n−4, obtaining analogues of some useful results known for the casen−1. In this setting we find some natural applications for the theory ofsigned groups and orthogonal matrices with entries from signed groups, as developed in [3]. We construct some new series of Hadamard matrices from weighing matrices, including the following:W(n, n−2) implies an Hadamard matrix of order2n ifn≡0 mod 4 and order 4n otherwise;W(n, n−3) implies an Hadamard matrix of order 8n; in certain cases,W(n, n−4) implies an Hadamard matrix of order 16n. We explicitly derive 117 new Hadamard matrices of order 2t p, p<4000, the smallest of which is of order 23·419.
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Craigen, R. The structure of weighing matrices having large weights. Des Codes Crypt 5, 199–216 (1995). https://doi.org/10.1007/BF01388384
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DOI: https://doi.org/10.1007/BF01388384