Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Two and Length pq

Pseudo-random sequences are used extensively for their high speed andsecurity level and less errors. As a branch, the cyclotomic sequencesand the generalized ones are studied widely because of their simplemathematical structures and excellent pseudo-random properties. In 1998,Ding and Helleseth introduced a new generalized cyclotomy whichincludes the classical cyclotomy as a special case. In this paper, basedon the generalized cyclotomy, new generalized cyclotomic sequences withorder two and length \it pq are constructed. An equivalent definition of thesequences is deduced so that the autocorrelation values of thesesequences can be determined conveniently. The construction contributesto the understanding of the periodic autocorrelation structure ofcyclotomically-constructed binary sequences, and the autocorrelationfunction takes on only a few values.