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

06/10/2021

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by   Vladimir Edemskiy, et al.

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R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (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.