It is known that Hall's sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period p. Here we study its correlation measure of order k and show that it is, up to a constant depending on k and some logarithmic factor, of order of magnitude p1/2, which is close to the expected value for a random sequence of length p. Moreover, we derive from this bound a lower bound on the Nth maximum order complexity of order of magnitude log p, which is the expected order of magnitude for a random sequence of length p.

The d-ary Sidel'nikov sequence S = s0, s1... of period q-1 for a prime power q=pmis a frequently analyzed sequence in the literature. Recently, it turned out that the linear complexity over Fpof the d-ary Sidel'nikov sequence is considerably smaller than the period if the sequence element s(q-1)/2mod(q-1)is chosen adequately. In this paper this work is continued and tight lower bounds on the linear complexity over Fpof the d-ary Sidel'nikov sequence are given. For certain cases exact values are provided. Finally, results on the k-error linear complexity over Fpof the d-ary Sidel'nikov sequence are presented.