Motivated by the constructions of binary sequences by utilizing the cyclic elliptic function fields over the finite field $\mathbb{F}_{2^{n}}$ by Jin \textit{et al.} in [IEEE Trans. Inf. Theory 71(8), 2025], we extend the construction to the cyclic elliptic function fields with odd characteristic by using the quadratic residue map $η$ instead of the trace map used therein. For any cyclic elliptic function field with $q+1+t$ rational points and any positive integer $d$ with $\gcd(d, q+1+t)=1$, we construct a new family of binary sequences of length $q+1+t$, size $q^{d-1}-1$, balance upper bounded by $(d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+d,$ the correlation upper bounded by $(2d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+2d$ and the linear complexity lower bounded by $\frac{q+1+2t-d-(d+1)\cdot\lfloor2\sqrt{q}\rfloor}{d+d\cdot\lfloor2\sqrt{q}\rfloor}$ where $\lfloor x\rfloor$ stands for the integer part of $x\in\mathbb{R}$.

翻译：受Jin等人[IEEE Trans. Inf. Theory 71(8), 2025]利用有限域$\mathbb{F}_{2^{n}}$上的循环椭圆函数域构造二进制序列的启发，我们将其构造推广至奇特征的循环椭圆函数域，其中使用二次剩余映射$η$替代原文中的迹映射。对于任意具有$q+1+t$个有理点的循环椭圆函数域，以及任意满足$\gcd(d, q+1+t)=1$的正整数$d$，我们构造了一类新的二进制序列族，其长度为$q+1+t$，规模为$q^{d-1}-1$，平衡度上界为$(d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+d$，相关值上界为$(2d+1)\cdot\lfloor2\sqrt{q}\rfloor+|t|+2d$，线性复杂度下界为$\frac{q+1+2t-d-(d+1)\cdot\lfloor2\sqrt{q}\rfloor}{d+d\cdot\lfloor2\sqrt{q}\rfloor}$，其中$\lfloor x\rfloor$表示$x\in\mathbb{R}$的整数部分。