Linear complexity of Legendre-polynomial quotients

Let p be an odd prime and w < p be a positive integer. The authors continue to investigate the binary sequence (f(u)) over {0, 1} defined from polynomial quotients by (uw -uwp)/p modulo p. The (f(u)) is generated in terms of (- 1) f(u) which equals to the Legendre symbol of (uw -uwp)/p (mod p) for u = 0. In an earlier work, the linear complexity of (f(u)) was determined for w = p - 1 (i. e. the case of Fermat quotients) under the assumption of 2(p-1) /= 1(mod p2). In this work, they develop a naive trick to calculate all possible values on the linear complexity of (f(u)) for all 1 = w < p - 1 under the same assumption. They also state that the case of larger w(= p) can be reduced to that of 0 <= w <= p - 1. So far, the linear complexity is almost determined for all kinds of Legendre-polynomial quotients.