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On decimations of \(\ell\)-sequences. (English) Zbl 1114.11015

Summary: Maximal length feedback with carry shift register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large and, in some cases, all decimations are distinct.

MSC:

11B50 Sequences (mod \(m\))
11L05 Gauss and Kloosterman sums; generalizations
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
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