The Propus Construction for Symmetric Hadamard Matrices

arXiv1512.01732MaRDI QIDQ6268091

N. A. Balonin, Jennifer Seberry

Publication date: 5 December 2015

Abstract: extit{Propus} (which means twins) is a construction method for orthogonal $pm1$ matrices based on a variation of the Williamson array called the extit{propus array} [ �egin{matrix*}[r] A& B & B & D B& D & -A &-B B& -A & -D & B D& -B & B &-A. end{matrix*} ] This construction designed to find symmetric Hadamard matrices was originally based on circulant symmetric $pm1$ matrices, called extit{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 extit{ Generalized Propus Array (GP)}.

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20)

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