On the 2-Adic Complexity of the Two-Prime Generator

Abstract

Hu introduced a simple method to compute the 2-adic complexity of any periodic binary sequence with ideal two-level autocorrelation. We extend this approach to some other sequences. First, we provide a substantially shorter proof of the maximality of the 2-adic complexity of the Legendre sequence of period $N\equiv 1\bmod 4$ first proved by Xiong et al . Then, we show that the 2-adic complexity of the two-prime generator of period $pq$ with two odd primes $p\ne q$ attains the maximum if $(q+1)/4\le p\le 4q-1$ . This result was only known for twin primes $q=p+2$ before. For arbitrary odd primes $p\ne q$ , we can still prove that the 2-adic complexity of the two-prime generator is close to its period.