Document Type
Journal Article
Abstract
We introduce Legendre sequences and generalised Legendre pairs (GL-pairs). We show how to construct an Hadamard matrix of order 2ℓ+2 from a GL-pair of length ℓ. We review the known constructions for GL-pairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable an exhaustive search for GL-pairs for lengths ℓ≤45 and partial results for other ℓ.
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Publication Details
Roderick J Fletcher, Marc Gysin and Jennifer Seberry, Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices, Australasian Journal of Combinatorics 23 (2001) 75-86.