On discrete Fourier transform,ambiguity, and Hamming-autocorrelation of pseudorandom sequences |
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Authors: | Gottlieb Isabel Pirsic Arne Winterhof |
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Affiliation: | 1. Financial Mathematics Institute, Johannes Kepler University Linz, Altenbergerstr. 69, 4040?, Linz, Austria 2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040?, Linz, Austria
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Abstract: | We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of (m) -ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conversely, there are sequences, for example the two-prime generator, with large correlation measure of order 4 but small discrete Fourier transform, ambiguity, autocorrelation, and Hamming-autocorrelation. |
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