Computer construction conjecture for symmetric hadamard matrices

Authors

N A. Balonin, Saint-Petersburg State University of Aerospace InstrumentationFollow
Jennifer Seberry, University of WollongongFollow

RIS ID

132642

Publication Details

Balonin, N. A. & Seberry, J. (2018). Computer construction conjecture for symmetric hadamard matrices. The Mathematical Scientist, 43 (2), 137-143.

Link to publisher version (URL)

Applied Probability Trust

Abstract

We consider and compare methods for computer construction of variously structured plug-in matrices (suitable matrices) used to construct skew-Hadamard matrices from the Goethals-Seidel array and symmetric Hadamard matrices from the Balonin-Seberry array. We call symmetric analogue matrices of suitable matrices for computer construction of skew-Hadamard matrices luchshie matrices (luchshie is the Russian plural for 'best'). We provide tables of known inequivalent luchshie matrices of order 4, n < 53, and symmetric Hadamard matrices of order 4n, n < 400. We propose the conjecture that there exist luchshie (±1) matrices of order odd t for all t. Hence, there exists a symmetric Hadamard matrix of order At for every odd t.