Binary Sequences Derived From Differences of Consecutive Primitive Roots
Arne Winterhof, Zibi Xiao · IEEE Transactions on Information Theory · 2021
Let 11φ(p-1)n) defined by sn≡ gn+1+gn+2mod 2, n=0,1,⋯ In particular, we study the balance, linear complexity and 2-adic complexity of (sn). We show that for a typical p the sequence (sn) is quite unbalanced. However, there are still infinitely many p such that (sn) is very balanced. We also prove similar results for the distribution of longer patterns. Moreover, we give general lower bounds on the linear complexity and 2-adic complexity of (sn) and state sufficient conditions for attaining their maximums. Hence, for carefully chosen p, these sequences are attractive candidates for cryptographic applications.