On pseudorandom binary sequences constructed by using finite fields (Q313474)

The author considers pseudorandom binary sequences constructed by finite fields and their quadratic characters. The results provide upper bounds for the well-distribution measure, for the correlation measure of order \(k\) and for the so-called \(PR\)-measure of order \(k\). In a first part a useful survey on results of Mauduit-Sárközy, Sárközy-Winterhof and of Gyarmati is presented. The second part contains extensions of Gyarmati's result and a sharpening of estimates due to Sárközy and Winterhof. The paper concludes with a list of open problems in this field.