In this letter, we give a new construction of a family of sequences of period pk-1 with low correlation value by using additive and multiplicative characters over Galois rings. The new constructed sequence family has family size (M-1)(pk-1)rpkr(e-1) and alphabet size Mpe. Based on the characters sum over Galois rings, an upper bound on the correlation of this sequence family is presented.

Primitive linear recurring sequences over rings are important in modern communication technology, and character sums of such sequences are used to analyze their statistical properties. We obtain a new upper bound for the character sum of primitive sequences of order n over the residue ring modulo a square-free odd integer m, and thereby improve previously known bound mn/2.

Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums. A lower bound on the linear complexity profile is also presented in terms of the correlation measure.