Lower bounds on the linear complexity of the discrete logarithm in finite fields

Let p be a prime, r a positive integer, q=p^r, and d a divisor of p(q-1). We derive lower bounds on the linear complexity over the residue class ring Z_d of a (q-periodic) sequence representing the residues modulo d of the discrete logarithm in F_q . Moreover, we investigate a sequence over F_q representing the values of a certain polynomial over F_q introduced by Mullen and White (1986) which can be identified with the discrete logarithm in F_q via p-adic expansions and representations of the elements of F_q with respect to some fixed basis