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.~Sárkzy 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).