Weight Measure Of Pseudorandom Binary Sequences And Lattices

Recently,many scholars have studied the statistical properties of pseudoran-dom sequences and constructed some pseudorandom sequences.In cryptography one needs pseudorandom sequences whose short subsequences are also pseudo-random.To handle this problem,Dartyge,Gyarmati and Sarkozy introduced weighted measures of pseudorandomness of binary sequences.In this paper we study the weighted measures of pseudorandomness of binary subsequences.Then,we introduce weighted pseudorandom measure for multi-dimensional bina-ry lattices.We also analyze the pseudorandomness for multi-dimensional binary sublattices and constuct a large family of multi-dimensional sublattice.Main results are as follows:Firstly,we study the weighted measures of pseudorandomness of general binary sequences by using the estimate of character sum and exponential sum.Moreover,we give the upper bounds of them.Secondly,we estimate weighted pseudorandom measure for truly random binary lattices by borrowing the Chernoff's inequality and number theory.Furthermore,we also give lower bounds for weighted measure of 2-order and different order multidimensional lattices by using the method of reference[2].Finally,we present an example by using the quadratic character of finite fields.