Researches On Ternary Sequences Of Generalized Cyclotomy

Pseudo-random sequences, with their good properties, have a wide range of applications ininformation security, communications and other areas, therefore, constructing pseudo-randomsequences with good properties has become the researching object of many scholars, especially at thistime when binary sequences researching has already become more and more perfect. In recent years,ternary sequences and q-ary sequences also attracted more and more researchers because of theirimportant applications in the fields of coding and cryptography, communications and so on.Based on the research on binary sequences, and using the cyclotomy theory, this article constructsseveral kinds of ternary sequences and studies their relevant properties. The main results are listed asfollows:（1） The D-generalized cyclotomic sequence of order six with periodpⁿ⁺¹over GF（3）which posses high linear complexity, where p=6f+1and f is even.（2） The generalized cyclotomic sequence of order four with period p over GF （3）which hasa four-valued autocorrelation function, where p=4m+1and m is even. By adding somerestrictions on the parameters, one can make the autocorrelation value reduced to3values.（3） The W-generalized cyclotomic sequence of order six with period pq over GF （3）whichhas good linear complexity, where gcd（p-1, q-1）6and p,q are odd primes.