, Volume 4, Issue 3, pp 327-340

On sequences with zero autocorrelation

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Abstract

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

Base sequences of lengths 2n−1, 2n−1,n,n are constructed for all decompositions of 6n−2 into four squares forn=2, 4, 6, ..., 20 and some base sequences forn=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.