Linear complexity and correlation of a class of binary cyclotomic sequences

摘要

Let p_1, p_2, . . ., p_n be distinct odd primes and let e_1, e_2, . . ., e_n be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140–166, 1998), a binary cyclotomic sequence of period p_1~(e1) p_2~(e2) . . . p_n~(en) is defined and denoted by s?. The linear complexity of s? is determined and is proved to be greater than or equal to (p_1~(e1) p_2~(e2) . . . p_n~(en) ? 1)/2. The autocorrelation function of s? is explicitly computed. Let ? ∈ {1, 2, . . ., n}. We also explicitly compute the crosscorrelation function of s? and the Legendre sequence L_(p?) with respect to p?. It is shown that s? and L_(p?) have two-level or three-level crosscorrelation, and all their two-level crosscorrelation functions are determined.