Construction of large families of pseudorandom binary sequences (Q5907098)

The authors continue their investigations on pseudorandom binary sequences. They consider the well-distribution measure and the correlation measure of order \(k\). Earlier they showed that the Legendre symbol forms a ``good'' pseudorandom sequence, and they also tested other sequences for pseudorandomness, however, no large family of ``good'' pseudorandom sequences has been found yet. In this paper, a large family of this type is constructed by extending the earlier Legendre symbol construction.