Sequences related to Legendre/Jacobi sequences

Two families of binary sequences are constructed from dth order cyclotomic generator and from dth order generalized cyclotomic generator with respect to two distinct primes respectively. By using estimates of certain exponential sums over rings or fields, the upper bounds of both the well-distribution measure and the order k (at least for small k) correlation measure of the resulting binary sequences are evaluated, and some lower bounds on the linear complexity profile of d-ary cyclotomic sequences and d-ary generalized cyclotomic sequences are presented. Our results indicate that such binary sequences possess “very good” local pseudo-randomness.