In this paper, we consider quaternary sequences of length pq, where p and q are two different odd primes. These sequences are constructed based on Legendre symbol and have low autocorrelation and high linear complexity. We derive the symmetric 4-adic complexity of these sequences and show that it is good enough to resist the attack of the rational approximation algorithm.

Abstract The arithmetic correlations of two binary half‐ ℓ ‐sequences with connection integer p r , which is an odd prime power, are investigated. Possible values (of the arithmetic correlation) are calculated. In particular, if p ≡ 1 (mod 8), the authors prove that they are zero for non‐trivial shifts, that is, the half‐ ℓ ‐sequences have ideal arithmetic correlations. If p ≡ −1 (mod 8), an upper bound, which is of order of magnitude p r −1/2 ln p , is derived by using earlier results on the imbalance of half‐ ℓ ‐sequences with connection integer p studied by Gu and Klapper and later improved by Wang and Tan.

In this paper, we consider two kinds of quaternary sequences, i.e., quaternary classical cyclotomic sequences with period q where q is an odd prime, and quaternary Ding-Helleseth generalized cyclotomic sequences with period pq where p is odd prime distinct from q. Then, using the generalized "Gauss periods", we derive 4-adic complexity of these sequences for any p,q and the results show that they have high symmetric 4-adic complexity.

In this paper, we consider the quaternary sequences with period pq where p and q are two odd primes. These sequences are constructed by interleaving the quaternary power residue sequence of period p according to the quadratic residue with respect to q. We derive the linear complexity of these sequences over the finite field of order four and the finite ring of order four. It is shown that the considered quaternary sequences have a sufficiently large linear complexity to resist Berlekamp-Massey algorithm or Reeds and Sloane algorithm attack effectively.

We examine the linear complexity and the autocorrelation of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.