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Computer construction conjecture for symmetric hadamard matrices

Journal Article


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.

Publication Date


  • 2018

Citation


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

Scopus Eid


  • 2-s2.0-85059676870

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2285

Number Of Pages


  • 6

Start Page


  • 137

End Page


  • 143

Volume


  • 43

Issue


  • 2

Place Of Publication


  • United Kingdom

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.

Publication Date


  • 2018

Citation


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

Scopus Eid


  • 2-s2.0-85059676870

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2285

Number Of Pages


  • 6

Start Page


  • 137

End Page


  • 143

Volume


  • 43

Issue


  • 2

Place Of Publication


  • United Kingdom