Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices

@article{Fletcher2001ApplicationOT,
  title={Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices},
  author={Roderick J. Fletcher and Marc Gysin and Jennifer Seberry},
  journal={Australasian J. Combinatorics},
  year={2001},
  volume={23},
  pages={75-86}
}
We introduce Legendre sequences and generalised Legendre pairs (G Lpairs). We show how to construct an Hadamard matrix of order 2£ + 2 from a GL-pair of length f. We review the known constructions for GLpairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable an exhaustive search for GL-pairs for lengths f ::::; 47 and partial searches for other f, 1 Definitions and Notation Let U be a sequence of e real numbers Uo, Ul, .'" U£-l' The periodic autocorrelation… CONTINUE READING

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