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Compositional Modeling: Finding the Right Model for the Job
, 1991
"... Faikenhainer, B. and K.D. Forbus, Compositional modeling: finding the right model for the job, Artificial Intelligence 51 ( 1991 ) 95143. ..."
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Cited by 271 (28 self)
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Faikenhainer, B. and K.D. Forbus, Compositional modeling: finding the right model for the job, Artificial Intelligence 51 ( 1991 ) 95143.
Application of the Discrete Fourier Transform to the Search for Generalised Legendre Pairs and Hadamard Matrices
 J. Combin
, 2001
"... We introduce Legendre sequences and generalised Legendre pairs (GLpairs). We show how to construct an Hadamard matrix of order 2` + 2 from a GLpair of length `. We review the known constructions for GLpairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable ..."
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Cited by 10 (1 self)
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We introduce Legendre sequences and generalised Legendre pairs (GLpairs). We show how to construct an Hadamard matrix of order 2` + 2 from a GLpair of length `. 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 GLpairs for lengths ` 45 and partial results for other `. 1 Definitions and Notation Let U be a sequence of ` real numbers u 0 ; u 1 ; :::; u `\Gamma1 . The periodic autocorrelation function PU (j) of such a sequence is defined by: PU (j) = `\Gamma1 X i=0 u i u i+j mod ` ; j = 0; 1; :::; ` \Gamma 1: Two sequences U and V of identical length ` are said to be compatible if the sum of their periodic autocorrelations is a constant, say a, except for the 0th term. That is, PU (j) + P V (j) = a; j 6= 0: (1) (Such pairs are said to have constant periodic autocorrelation even though it is the sum of the autocorrelations that is a constant.) If U and V are both \Si...
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"... We introduce Legendre sequences and generalised Legendre pairs (GL{pairs). We show how to construct an Hadamard matrix of order 2 ` + 2 from a GL{pair of length `. We review the known constructions for GL{pairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable a ..."
Abstract
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We introduce Legendre sequences and generalised Legendre pairs (GL{pairs). We show how to construct an Hadamard matrix of order 2 ` + 2 from a GL{pair of length `. 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 ` 45 and partial results for other `. 1 Denitions and Notation Let U be a sequence of ` real numbers u