### On Correlations of A Family of Generalized Geometric Sequences

IEEE Transactions on Information Theory ** 47 ** (2001) 2609-2618.
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

Wei Sun, Yi Xian Yang, Beijing University of Posts and Telecommunications

**Abstract**
In this paper we study families of generalized geometric sequences formed
by applying a feedforward function to certain sums of decimated m-sequences
with elements in a finite field. We compute their correlation functions,
which for certain families turn out to be close to the square root of the
period. The size of these families equals their period. We also show
that in the binary case the linear complexities of these sequences are
much larger than those of cascaded geometric sequences, although in these
cases the maximum correlations are larger.

**Index Terms --**
Generalized geometric sequence, Correlation function, Character,
Linear complexity.