The linear complexity of a sequence is not only a measure for the unpredictability and thus
suitability for cryptography but also of interest in information theory because of its close …

Harald Niederreiter Arne Winterhof Page 1 Applied Number Theory Harald Niederreiter Arne
Winterhof Page 2 Applied Number Theory Page 3 Page 4 Harald Niederreiter • Arne Winterhof …

Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there
have been significant advancements on the topic of complexity measures for randomness …

We obtain some theoretical and experimental results concerning various properties (the
number of fixed points, image distribution, cycle lengths) of the dynamical system naturally …

The correlation measure of order k is an important measure of pseudorandomness for binary
sequences. This measure tries to look for dependence between several shifted versions of a …

We prove a bound on sums of products of multiplicative characters of shifted Fermat
quotients modulo p. From this bound we derive results on the pseudorandomness of …

Any permutation of a finite field Fq can be represented by a polynomial [Formula: see text],
for some n⩾ 0. P0 is linear and the cycle structure of P1 is known. In this work we present the …

We improve lower bounds on the k th-order nonlinear complexity of pseudorandom
sequences over finite fields, including explicit inversive sequences and sequences obtained …

A pseudorandom sequence is a repeatable sequence with random statistical properties that
is widely used in communication encryption, authentication and channel coding. The …

In the second half of the 1990s Christian Mauduit and András Sárközy [86] introduced a new
quantitative theory of pseudorandomness of binary sequences. Since then numerous …