2015/12/06 by Jennifer Seberry, Seberry, Jennifer, N. A. Balonin +1
Mathematics · #05B20 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B20
paper · pdf · doi:10.48550/arxiv.1512.01732
13 pages, 19 figures
arxiv created 2015/12/06 · arxiv updated 2015/12/08
Propus (which means twins) is a construction method for orthogonal ± 1 matrices based on a variation of the Williamson array called the propus array \beginmatrix*[r] A B B D B D -A -B B -A -D B D -B B -A. \endmatrix* This construction designed to find symmetric Hadamard matrices was originally based on circulant symmetric ± 1 matrices, called propus matrices. We also give another construction based on symmetric Williamson-type matrices. We give constructions to find symmetric propus-Hadamard matrices for 57 orders 4n, n < 200 odd. We give variations of the above array to allow for more general matrices than symmetric Williamson propus matrices. One such is the Generalized Propus Array (GP).