On the 4-adic complexity of the two-prime quaternary generator

Abstract

R. Hofer and A. Winterhof proved that the 2-adic complexity of the twoprime (binary) generator of period pq with two odd primes p = q is close to its period and it can attain the maximum in many cases.When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. We present the formulae of possible values of the 4-adic complexity, which is larger than pq − log 4 (pq 2 ) − 1 if p < q. So it is good enough to resist the attack of the rational approximation algorithm.