The pseudorandom properties of finite binary sequences have been studied recently intensively. In the papers written on this
subject the two distinct elements of the sequences are chosen equally with probability 1/2. In this paper the authors extend the work to the more general case when the two elements are chosen with probability p, resp. 1-p.
In the applications it may occur that our initial pseudorandom binary sequence turns out to be not long enough, thus we have
to take the concatenation or merging of it with other pseudorandom binary sequences. Here our goal is study when we can form
the concatenation of several pseudorandom binary sequences belonging to a given family? We introduce and study new measures
which can be used for answering this question.
Using the discrete logarithm in  and  a large family of pseudorandom binary sequences was constructed. Here we extend
this construction. An interesting feature of this extension is that in certain special cases we get sequences involving points
on elliptic curves.
Summary By using the multiplicative inverse modulo p, a large family of finite binary sequences is constructed with strong pseudorandom properties. The crucial tool in the proofs is an (additive) character sum estimate of Eichenauer--Hermann and Niederreiter.
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.
In this paper a large family of pseudorandom binary lattices is constructed by using the multiplicative characters of finite
fields. This construction generalizes several one-dimensional constructions to arbitrary dimensions.
In a series of papers Mauduit and Sárközy (partly with coauthors) studied finite pseudorandom binary sequences and they constructed
sequences with strong pseudorandom properties. In these constructions fields with prime order were used. In this paper a new
construction is presented, which is based on finite fields of order 2k.