FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 1083-1094

**Bounds for the number of occurrences of elements in a linear
recurring sequence over a Galois ring**

O. V. Kamlovsky

A. S. Kuzmin

Abstract

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The number of occurrences of $r$-tuples in the cycle
of a linear recurring sequence over a Galois ring is
considered.
In the special case when the characteristic polynomial of
linear recurring sequence is a monic basic irreducible
polynomial, we give an upper bound for modulus of difference
between the number of occurrences of $r$-tuples in the linear
recurring sequence and uniform distributed sequence.
In some cases this bound is better than other results which have been
obtained for linear recurring sequences of maximal period over residue
rings of primary order.

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Last modified: February 13, 2001