The upper bound of crosscorrelation of M-sequences which have the same period but different characteristic polynomials is shown theoretically.
An M-sequence generated by an
n-th degree characteristic polynomial which is a primitive polynomial over GF(2) is constructed, in case of the period
N=2
n-1 is nonprime, by the combinations of
s nonmaximum length sequences with length
q generated by an
n-th degree irreducible polynomial of exponent
q, where
q=N/s and
s is a positive integer and
q>s. Therefore the primitive polynomials can be classified into the same class, if the nonmaximum length sequences are the same under the sampling of every
s bits from the original M-sequences.
Using this classification, it is shown that the crosscorrelation between the M-sequences in the same class is larger than that of other M-sequences. The crosscorrelation function is obtained by the weights of the nonmaximum length sequences. And the maximum crosscorrelation value appears at the delay time of an integral multiple of
q, when the two M-sequences are relatively phased so as for the initialpoints characteristic M-sequences to coincide, and then the crosscorrelation function is calculated with the delay taken from that phase.
The upper bounds of the crosscorrelation function of different M-sequences in case of
s=5 and 7 are obtained.
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