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Pseudo-random sequences are used extensively for their high speed and security level and less errors.As a branch,the cyclotomic seqnences and the generalized ones are studied widely because of their simple mathematical structures and excellent pseudo-random properties.In 1998,Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case.In this paper,based on the generalized cyclotomy,new generalized cyclotomic sequences with order two and length pq are constructed.An equivalent definition of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently.The construction contributes to tile understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences,and the autocorrelation function takes on only a few values.
Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic seqnences and the generalized ones are widely because of their simple mathematical structures and excellent pseudo-random properties. In 1998, Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case. In this paper, based on the generalized cyclotomy, new generalized cyclotomic sequences with order two and length pq are constructed. An equivalent equivalent of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently. The construction contributes to tile understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences, and the autocorrelation function takes on only a few values.