Linear Complexity and 2-Adic Complexity of New Cyclotomic Binary Sequences of Order Four with Low Autocorrelation

A new family of binary sequences with low 4-value autocorrelation of length 4p based on cyclotomic classes of order four is proposed, as well as the linear complexity and 2-adic complexity of these sequences are determined. The results show that the linear complexity of s is LC(s) = 4p−1, and the 2-adic complexity of s is Φ2s = log2 ((24p−1)/3), both of which are greater than half of the period. The sequences are safe enough to resist Berlekamp–Massey algorithm attacks and rational approximation algorithm attacks, which indicate that they are good sequences in communication.