M-sequence Triple Correlation Function Co-set Summing and Code Image Print (CIP)

It is known that for the Time-Frequency analysis, the variants of short time Fourier transform can be used for detection of the information data. In this paper, a study of the properties of the triple correlation function (tcf) of the M-Sequence codes will be introduced; the M-sequences with code length equal to 127 bits have been given attention in this paper and considered as a good representative for other M-sequences with different lengths. The results of the codes tcf will be introduced to obtain and verify the "Doubling Process" property of the M-sequences. In addition, the Co-Set summing of the tcf will be explained and how we can use the results of the summing process to lead us to the code footprint or what we can call Code Image Print (CIP) that will be the key point for code identification.