### On Decimations of l-Sequences

SIAM Journal on Discrete Math, ** 18** (2004) 130-140.
Authors:

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science,
University of Kentucky, Lexington, KY, 40506-0046, klapper at cs.uky.edu.
www.cs.uky.edu/~klapper/andy.html

Mark Goresky, Institute for Advanced Study

Ram Murthy, Queen's University

Igor Shparlinski, Macquarie University

**Abstract**
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.

**Index Terms --**
feedback with carry shift register, arithmetic correlation,
exponential sum, binary sequence, p-adic number.