We present mosaic theorem for binary sequence and multiple sampling sequence. Main conclusion includes: multiple sampling sequence has nothing to do with its original state, and g(x<sup>N1) is one of itsgenerator polynomial, and there is a SSCO that its minimum polynomial mc(x)=g(x<sup>N1); When the number of “1” is power of 2 in the controlled sequence, the minimum polynomial of multiple sampling sequence is gt(x), its period is 2r(2n-1); Specially, When the controlled sequence is m-Sequence and (m,n)=1,m≤n/2, the minimum polynomial of multiple sampling sequence is mc(x)=gt(x), its period is 2m-1(2n-1),2m-2＜t≤2m-1.
