Collision and avalanche effect in families of pseudorandom binary sequences

Recently a constructive theory of pseudorandomness of binary sequences has been developed and many constructions for binary sequences with strong pseudorandom properties have been given. In the applications one usually needs large families of binary sequences of this type. In this paper we adapt the notions of collision and avalanche effect to study these pseudorandom properties of families of binary sequences. We test two of the most important constructions for these pseudorandom properties, and it turns out that one of the two constructions is ideal from this point of view as well, while the other construction does not possess these pseudorandom properties.