抄録
The cross-correlation of m-sequences which have the same period but different characteristic polynomials is shown theoretically.
When the order N of a primitive element α in GF(2n) is nonprime, it is represented by N=sq(s, q, integer). Therefore an irreducible polynomial of degree n of exponent q with a root αs must exist. If each root of the two different primitive polynomials is denoted as αa, αb, the primitive polynomials can be classified into a set of primitive polynomials in such a way that sa, sb modulo N belong to the same coset. This means that the two m-sequences are classified into the same class if they become the same sequence under the sampling of s bits.
By the use of characteristic m-sequences it is shown that the cross-correlation between the different m-sequences generated by primitive polynomials of the same class becomes large when the delay is an integral multiple of q. This is due to the fact that the cross-correlation sequence contains the non-maximum length sequences generated by its irreducible polynomial.
The cross-correlation values in case of s=3 are analyzed and obtained explicitly. The cross-correlation values actually obtained agree well with the theoretical ones.
