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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 $n=2,4,6,\cdots ,20$ 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.

##### MSC:
 05B20 Matrices (incidence, Hadamard, etc.) 68R05 Combinatorics in connection with computer science 62H20 Statistical measures of associations
##### References:
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