Kravvaritis, C; Mitrouli, M; and Seberry, Jennifer, 2005, On the growth problem for skew and symmetric conference matrices, Linear Algebra and Its Applications, 403, 183-206.
Koukouvinos et al. [C. Koukouvinos, M. Mitrouli, J. Seberry, Growth in Gaussian elimination for weighing matrices, W(n,n − 1), Linear Algebra Appl. 306 (2000) 189–202], conjectured that the growth factor for Gaussian elimination of any completely pivoted weighing matrix of order n and weight n − 1 is n − 1 and that the first and last few pivots are (1, 2, 2, 3 or 4, . . . , n − 1 or n−1/2 , n−1/2 , n − 1) for n > 14. In the present paper we study the growth problem for skew and symmetric conference matrices. An algorithm for extending a k × k matrix with elements 0, ±1 to a skew and symmetric conference matrix of order n is described. By using this algorithm we show that the unique W(8, 7) has two pivot structures. We also prove that the unique W(10, 9) has three pivot patterns.