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Cyclotomy theory on residue class ring has widely been used in the design of sequences and the construction of communication codes. According to the known research achievements, binary Whiteman generalized cyclotomic sequences of orders 2 and 4 over the two-prime residue ring have a number of good randomness properties. Based on cyclotomy on the two-prime residue ring and the Chinese Remainder Theorem, by making a binary segmentation of the residue class ring and applying characteristic set method, this paper constructs a class of binary Whiteman generalized cyclotomic sequences of order 6 of two-prime period . Then, according to the polynomial theory on finite fields, by constructing the splitting field of the polynomial and discussing different values of and , the corresponding linear complexities (linear span) of these sequences are calculated. Our results show that the least value of their linear complexities is , which meet the cryptographic requirement. In addition, we calculate the autocorrelation values of some binary generalized cyclotomic sequences of order 6 constructed in this paper by making use of the Whiteman cyclotomic numbers of order 6 and the differential function. Other situations can also be obtained in the same way.
