Binary Sequences With a Low Correlation via Cyclotomic Function Fields of Odd Characteristic

Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths, where binary sequences attract great attention. As a result, various constructions of good binary sequences have been proposed. However, most of the known constructions made use of the multiplicative cyclic group structure of finite field Fpn for a prime p and a positive integer n. In fact, all pn + 1 rational places including the place at infinity of the rational function field over Fpn can form a cyclic structure under an automorphism of order pn + 1. In this paper, we make use of this cyclic structure to provide an explicit construction of binary sequences with a low correlation of length pn + 1 via cyclotomic function fields over Fpn for any odd prime p. Each family of binary sequences has size pn- 2 and its correlation is upper bounded by 4+.2 center dot pn/2.. To the best of our knowledge, this is the first construction of binary sequences with a low correlation of length pn + 1 for odd prime p. Moreover, our sequences can be constructed explicitly and have competitive parameters.