Motivated by the constructions of pseudorandom sequences over the cyclic elliptic function fields by Hu \textit{et 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 \textit{et 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].

翻译：受 Hu 等人于 [IEEE Trans. Inf. Theory, 53(7), 2007] 中在循环椭圆函数域上构造伪随机序列的工作，以及 Xing 等人于 [IEEE Trans. Inf. Theory, 49(6), 2003] 中从函数域构造低相关性、大线性复杂度的二进制序列的工作的启发，我们利用 Weil [Basic Number Theory, Grund. der Math. Wiss., Bd 144] 和 Deligne [Lecture Notes in Mathematics, vol. 569 (Springer, Berlin, 1977)] 为一般代数函数域上的指数和所推导的界，研究了一类 $p$ 元序列的周期、线性复杂度、线性复杂度轮廓、$r-$模式的分布、周期相关性以及非线性复杂度。该类序列推广了 [IEEE Trans. Inf. Theory, 49(6), 2003] 和 [IEEE Trans. Inf. Theory, 53(7), 2007] 中的构造。