A large family of sequences with low correlation
Zhangti Yan, Qi Gao, Wei Min Guo, Rong Luo · 2022
In this paper, for a prime$p$and positive integers$n, m, e$, and$t$such that$n=2me$and$t=\lfloor\frac{m}{2}\rfloor$, a new large family$\mathcal{S}$of p-ary sequences of period$p^{n}-1$with low correlation is constructed. It is shown that$\mathcal{S}$has maximum correlation magnitude$1+p^{\frac{n}{2}+2te-e}$, family size$p^{nt}$and maximal linear span$(t+1)n$. Furthermore, based on the theory of quadratic forms over finite fields, all exact correlation values between sequences in$\mathcal{S}$are determined when$p = 2$.