Goresky, Mark; Klapper, Andrew; Murty, M. Ram; Shparlinski, Igor On decimations of \(\ell\)-sequences. (English) Zbl 1114.11015 SIAM J. Discrete Math. 18, No. 1, 130-140 (2004). 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. Cited in 1 ReviewCited in 5 Documents 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 Keywords:feedback with carry shift register; arithmetic correlation; exponential sum; binary sequence; \(p\)-adic number PDFBibTeX XMLCite \textit{M. Goresky} et al., SIAM J. Discrete Math. 18, No. 1, 130--140 (2004; Zbl 1114.11015) Full Text: DOI