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On sequences with zero autocorrelation. (English) Zbl 0808.05021

Summary: Normal sequences of lengths n=18,19 are constructed. It is proved through an exhaustive search that normal sequences do not exist for n=17,21,22,23. Marc Gysin has shown that normal sequences do not exist for n=24. So the first unsettled case is n=27.

Base sequences of lengths 2n-1,2n-1,n,n are constructed for all decompositions of 6n-2 into four squares for n=2,4,6,,20 and some base sequences for n=22,24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461, 6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869.

05B20Matrices (incidence, Hadamard, etc.)
68R05Combinatorics in connection with computer science
62H20Statistical measures of associations
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