报告题目 (Title)：椭圆曲线上一类低相关度的二元序列的构造（A new family of binary sequences with low correlation via elliptic curves）
报告人 (Speaker)： 马立明 研究员（中国科学技术大学）
报告时间 (Time)：2025年9月25日(周四) 14：00
报告地点 (Place)：腾讯会议 354 281 882
邀请人(Inviter)：丁洋
报告摘要：In the realm of modern digital communication, cryptography, and signal processing, binary sequences with good correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good binary sequences of various lengths. As a consequence, numerous constructions of good binary sequences have been put forward. However, the majority of known constructions leverage the multiplicative cyclic group structure of finite fields $\mathbb{F}_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Recently, the authors made use of the cyclic group structure of all rational places of the rational function field over the finite field $\mathbb{F}_{p^n}$, and firstly constructed good binary sequences of length $p^n+1$ via cyclotomic function fields over $\mathbb{F}_{p^n}$ for any prime $p$. This approach has paved a new way for constructing good binary sequences. Motivated by the above constructions, we exploit the cyclic group structure of rational points of elliptic curves to design a family of binary sequences of length $2^n+1+t$ with low correlation for many given integers $|t|\le 2^{(n+2)/2}$. Specifically, for any positive integer $d$ with $\gcd(d,2^n+1+t)=1$, we introduce a novel family of binary sequences of length $2^n+1+t$, size $q^{d-1}-1$, correlation bounded by $(2d+1) \cdot 2^{(n+2)/2}+ |t|$, and large linear complexity via elliptic curves.