The design of large family size with the optimal cross-correlation property is important in spread spectrum and code division multiple access communication systems. In this paper we present the sequences with the decimation $d=2{cdot}2^m-1$, calculate the cross-correlation spectrum for $0{leq}t{leq}2^n-2$ and count the number of the value $2^m-1$ occurring for $0{leq}{ au}2^n-2$. The sequences have the optimal cross-correlation property. The work on this paper can make it easier to count the number of the whole value occurring for $0{leq}{ au}2^n-2$.