A New Family of Binary Sequences With Low Correlation via Elliptic Curves
Lingfei Jin, Liming Ma, Chaoping Xing, Runtian Zhu · IEEE Transactions on Information Theory · 2025
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 Fpn, wherepis a prime andnis 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 Fpn, and firstly constructed good binary sequences of lengthpn+ 1 via cyclotomic function fields over Fpnfor any primep[8], [10]. 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 2n+1+twith low correlation for many given integers |t| ⩽ 2(n+2)/2. Specifically, for any positive integerdwith gcd(d; 2n+1+t) = 1, we introduce a novel family of binary sequences of length 2n+1+t, sizeqd−1− 1, correlation bounded by (2d+ 1) · 2(n+2)/2+ |t|, and large linear complexity via elliptic curves.