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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Construction of Proper Higher Dimensional Hadamard Matrices from Perfect Binary Arrays

K. J. Horadam1, Cantian Lin1
1 Department of Mathematics, Royal Melbourne Institute of Technology, Melbourne, VIC 3001, Australia.
  • Published: 31/10/1998

Abstract

We describe several techniques for constructing \(n\)-dimensional Hadamard matrices from \(2\)-dimensional Hadamard matrices, and note that they may be applied to any perfect binary array \((PBA)\), thus optimally improving a result of Yang. We introduce cocyclic perfect binary arrays, whose energy is not restricted to being a perfect square. These include
all of Jedwab’s generalized perfect binary arrays. There are many more cocyclic \(PBAs\) than \(PBAs\). We resolve a potential ambiguity inherent in the “weak difference set” construction of \(n\)-dimensional Hadamard matrices from cocyclic \(PBAs\) and show it
is a relative difference set construction.

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Citation
K. J. Horadam, Cantian Lin. Construction of Proper Higher Dimensional Hadamard Matrices from Perfect Binary Arrays[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 028. 237-248. DOI: .