Computing the 2-Adic Complexity of Two Classes Generalized Cyclotomic Sequences

Abstract

This paper contributes to analyze the 2-adic complexity of a class of Ding-Helleseth generalized cyclotomic sequences and a class of Whiteman generalized cyclotomic sequences of periods of $N=pq$ , where $p$ and $q$ are two odd distinct primes with $\mathrm {gcd}(p-1,q-1)=2$ satisfying $p\equiv q\equiv 3\pmod 4$ . The results show that the 2-adic complexity of these sequences is at least $pq-p-q-1$ . Then it is large enough to resist the attacks of rational approximation algorithm.

Keywords

• Cyclic matrix
• Whiteman generalized cyclotomic sequences
• Ding-Helleseth generalized cyclotomic sequences
• 2-adic complexity