@article{Rong2024, 
author = {Jianying Rong and Ting Li and Rui Hua and Xuemei Wang},
title = {A class of binary sequences with two-valued cross correlations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9091-9106},
keywords = {cross correlation, exponential sum},
url = {https://www.sciopen.com/article/10.3934/math.2024442},
doi = {10.3934/math.2024442},
abstract = {Let    p be an odd prime with    p  ≡  7    (  mod    12  ),              p      −      1        2   be the least integer such that        2                            p          −          1                2              ≡  1    (  mod    p  ), and    q  =      2                            p          −          1                2            . Let    α be a primitive element of the finite field              F              q       and    β  =      α                            q          −          1                p            . Suppose that    σ  =      ∑          i      =      0        2        β          m              ζ        3        i              ∈            F        q    ∗  , where    m  ∈            F        p    ∗   and        ζ    3   is a    3rd root of unity in              F        p  . Let    {      u    i    }  =  (      Tr          q              /            2        ⁡  (  σ      β    i    )      )          i      =      0              q      −      2       be a binary sequence of period    q  −  1. In this paper, we obtained the cross correlation distribution between two sequences    {      u    i    } and its              q      −      1        p  -decimation sequence, which is two-valued.}
}