On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.
We prove the existence of a limit distribution of the normalized well-distribution measure (as ) for random binary sequences , by this means solving a problem posed by Alon, Kohayakawa, Mauduit, Moreira and Rödl.