A class of pseudorandom sequences From Function Fields

Motivated by the constructions of pseudorandom sequences over the cyclic elliptic function fields by Hu $\mathit{\text{et}}\mathit{\text{al.}}$ in $\text{[IEEE Trans. Inf. Theory, 53(7), 2007]}$ and the constructions of low-correlation, large linear span binary sequences from function fields by Xing $\mathit{\text{et}}\mathit{\text{al.}}$ in $\text{[IEEE Trans. Inf. Theory, 49(6), 2003]}$, we utilize the bound derived by Weil $\text{[Basic Number Theory, Grund. der Math. Wiss., Bd 144]}$ and Deligne $\text{[ Lecture Notes in Mathematics, vol. 569 (Springer, Berlin, 1977)]}$ 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 $\text{[IEEE Trans. Inf. Theory, 49(6), 2003]}$ and [IEEE Trans. Inf. Theory, 53(7), 2007].