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

Symmetric 4-adic complexity of quaternary sequences with low autocorrelation and period $ pq $

“…According to ( 5) and ( 9) we get (iii) Finally, we study r = gcd S(4), 3(4 pq −1) (4 p −1)(4 q −1) . By ( 5) and ( 8) we get It is clear that (±4pq + c 2 + p) 2 > 4(c ± 4yq) 2 p. Hence, r divides (±4pq + c 2 + p) 2 − 4(c ± 4yq) 2 p. Since c 2 ≤ 9, it follows that r < 16p 2 (q + 1) 2 Now we show that gcd(S(4), 4 pq −1) = gcd(S(4), 4 q −1)•gcd(S(4),…”

“…The 4-adic complexity of series of interleaved quaternary sequences was investigated in [10,11]. Very recently, the 4-adic complexity of quaternary sequences with period equal to the product of two primes was studied in [2,19]. The sequences presented in [19] have not good autocorrelation property.…”

“…First, we estimate Φ 4 (s). According to (2), it is sufficient to study gcd(S(4), 4 pq − 1). Since p, q are different primes, it follows that gcd(4 p − 1, 4 q − 1) = 3.…”

Improvements on the 4-adic complexity of a class of quaternary sequences

“…In recent ten years, the research results of the 2-adic complexity of binary periodic sequences are rich [3,4,6,[15][16][17][18][19][20]25]. To the best of our knowledge, there are few literatures to study the 4-adic complexity of quaternary periodic sequences [2,13,14,21,22].…”