A class of pseudorandom sequences From Function Fields
Abstract
Motivated by the constructions of pseudorandom sequences over the cyclic elliptic function fields by Hu et al. in [IEEE Trans. Inf. Theory, 53(7), 2007] and the constructions of low-correlation, large linear span binary sequences from function fields by Xing et al. in [IEEE Trans. Inf. Theory, 49(6), 2003], we utilize the bound derived by Weil [Basic Number Theory, Grund. der Math. Wiss., Bd 144] and Deligne [ Lecture Notes in Mathematics, vol. 569 (Springer, Berlin, 1977)] for the exponential sums over the general algebraic function fields and study the periods, linear complexities, linear complexity profiles, distributions of r-patterns, period correlation and nonlinear complexities for a class of p-ary sequences that generalize the constructions in [IEEE Trans. Inf. Theory, 49(6), 2003] and [IEEE Trans. Inf. Theory, 53(7), 2007].