On a family of pseudorandom binary sequences

Recently, numerous constructions have been given for finite pseudorandom binary sequences. However, in many applications, e.g., in cryptography one needs “large’’ families of “good’’ pseudorandom sequences. Very Recently L.~Goubin, C.~Mauduit, A.~Sárkőzy succeeded in constructing large families of pseudorandom binary sequences based on the Legendre symbol. In this paper we will generate another type of large family of pseudorandom sequences by using the notion of index (discrete logarithm).