A class of binary sequences with two-valued cross correlations

Let p be an odd prime with p equivalent to 7 (mod 12), p-12 be the least integer such that 2p-12 equivalent to 1 (mod p), and q = 2p-1 2 . Let alpha be a primitive element of the finite field Fq and beta = alpha q-1 p . Suppose that sigma = Z2i=0 beta m zeta i3 is an element of F*q, where m is an element of F*p and zeta 3 is a 3rd root of unity in Fp. Let {ui} =(Trq/2(sigma beta i))q-2 i=0 be a binary sequence of period q - 1. In this paper, we obtained the cross correlation distribution between two sequences {ui} and its q-1 p -decimation sequence, which is two -valued.