A weighing matrix W = (wi,j) is a square of order n and entries wi,j in {0,± 1} such that WWT kIn. In his thesis, Strassler gave table existence results for circulant matrices with ≤ 200 k 100. the latest version Strassler’s given by Tan, there are 34 open cases remaining. this paper we give nonexistence proofs 12 these cases, report on preliminary searches outside table, characterize known pro...

Balanced weighing matrices with parameters $$\left({1 + 18 \cdot {{{9^{m 1}} - 1} \over 8},{9^{m 1}},4 {9^m}} \right),$$ for each nonzero integer m are constructed. This is the first infinite class not belonging to those classical parameters. It shown that any balanced matrix equivalent a five-class association scheme.

We verify the skew weighing matrix conjecture for orders 2t.7, t ~ 3 a positive integer, by showing that orthogonal (1, k) exist for all t k = 0, 1, .... , 2.7 1 in order 2t.7 We discuss the construction of orthogonal designs using circulant matrices. In particular we construct designs in orders 20 and 28. The weighing matrix conjecture is verified for order 60. Disciplines Physical Sciences an...

This file contains additional information relating to the article: “A Search for Solvable Weighing Matrices,” submitted to Journal of Combinatorial Mathematics and Combinatorial Computing Feb. 25, 2005. In that article, we describe a computer search for group-developed weighing matrices of order 60 and weight 25, which we abbreviate as W (60, 25). Generally speaking, we view weighing matrices a...

A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order 2n, weight 2n− k and spread σ, are constructed from two circulants matrices by using complementary sequences of zero non-periodic autocorrelation function, i.e. ternary complementary pairs. Moreover, ...

Williamson type matrices A, B, C 1 D will be called nice if ABT + C DT = 0, perfect if ABT + CDT = ACT + BDT 0, special if ABT + CDT = ACT + BDT = ADT + BCT = o. Type 1 (1 , -1 )-matrices A, B, C, D of order n will be called tight Williamson-like matrices if AAT + BBT + CCT + DDT 4nIn and ABT + BAT + CDT + DCT o. Write N = 32T . piTl ••• p!Tn , where Pj 3(mod 4), Pj > 3, j = 1, ... ,n and r, rl...

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...

In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrat...