Measures of pseudorandomness for binary sequences constructed using finite fields

We extend the results of Goubin, Mauduit and Sárközy on the well-distribution measure and the correlation measure of order kk of the sequence of Legendre sequences with polynomial argument in several ways. We analyze sequences of quadratic characters of finite fields of prime power order and consider in each case two, in general, different definitions of well-distribution measure and correlation measure of order kk, respectively.