Skip to main content
placeholder image

Two infinite families of symmetric hadamard matrices

Journal Article


Download full-text (Open Access)

Abstract


  • © 2017, University of Queensland. All rights reserved. A construction method for orthogonal ±1 matrices based on a variation of the Williamson array, first described by N. A. Balonin, on his web page mathscinet.ru/catalogue/propus/ where he called it the propus array, gives symmetric propus-Hadamard matrices using (Forumala presented). We show that: for q ≡ 1 (mod 4), a prime power, symmetric propus-Hadamard matrices exist for order 2(q + 1); and for q ≡ 1 (mod 4), a prime power, and ½(q + 1) a prime power or the order of the core of a symmetric conference matrix (this happens for q = 89), symmetric propus-type Hadamard matrices of order 4(2q + 1) exist. We give constructions to find symmetric propus-Hadamard matrices for 57 orders 4n, n < 200 odd.

Publication Date


  • 2017

Citation


  • Seberry, J. & Balonin, N. (2017). Two infinite families of symmetric hadamard matrices. Australasian Journal of Combinatorics, 69 (3), 349-357.

Scopus Eid


  • 2-s2.0-85030850732

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1783&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/782

Has Global Citation Frequency


Number Of Pages


  • 8

Start Page


  • 349

End Page


  • 357

Volume


  • 69

Issue


  • 3

Place Of Publication


  • Canada

Abstract


  • © 2017, University of Queensland. All rights reserved. A construction method for orthogonal ±1 matrices based on a variation of the Williamson array, first described by N. A. Balonin, on his web page mathscinet.ru/catalogue/propus/ where he called it the propus array, gives symmetric propus-Hadamard matrices using (Forumala presented). We show that: for q ≡ 1 (mod 4), a prime power, symmetric propus-Hadamard matrices exist for order 2(q + 1); and for q ≡ 1 (mod 4), a prime power, and ½(q + 1) a prime power or the order of the core of a symmetric conference matrix (this happens for q = 89), symmetric propus-type Hadamard matrices of order 4(2q + 1) exist. We give constructions to find symmetric propus-Hadamard matrices for 57 orders 4n, n < 200 odd.

Publication Date


  • 2017

Citation


  • Seberry, J. & Balonin, N. (2017). Two infinite families of symmetric hadamard matrices. Australasian Journal of Combinatorics, 69 (3), 349-357.

Scopus Eid


  • 2-s2.0-85030850732

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1783&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/782

Has Global Citation Frequency


Number Of Pages


  • 8

Start Page


  • 349

End Page


  • 357

Volume


  • 69

Issue


  • 3

Place Of Publication


  • Canada