Construction of large families of pseudorandom binary sequences

In a series of papers Mauduit and Sárközy (partly with coauthors) studied finite pseudorandom binary sequences. 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.