Hadamard matrices, finite sequences, and polynomials defined on the unit circle

Author:
C. H. Yang

Journal:
Math. Comp. **33** (1979), 688-693

MSC:
Primary 05B20; Secondary 15A57

DOI:
https://doi.org/10.1090/S0025-5718-1979-0525685-8

MathSciNet review:
525685

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Abstract: If a -type Hadamard matrix of order 2*n* (i.e. a pair (*A, B*) of circulant (1,-1) matrices satisfying ) exists and a pair of Golay complementary sequences (or equivalently, two-symbol -code) of length *m* exists, then a -type Hadamard matrix of order 2*mn* also exists. If a Williamson matrix of order 4*n* (i.e. a quadruple (*W, X, Y, Z*) of symmetric circulant (1,-1) matrices satisfying ) exists and a four-symbol -code of length *m* exists, then a Goethals-Seidel matrix of order 4*mn* (i.e. a quadruple (*A, B, C, D*) of circulant (1, -1) matrices satisfying ) also exists. Other related topics are also discussed.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0525685-8

Article copyright:
© Copyright 1979
American Mathematical Society