On Decimations of $\ell$-Sequences
Mark Goresky, Andrew Klapper, Ram Murty, Igor E. Shparlinski · SIAM Journal on Discrete Mathematics · 2004
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.