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A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${mathbb{F}_{{q}}}$ as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when $pequiv pm 1(bmod~8)$ and is equal to {$p$+1} when $pequiv pm 3(bmod~8)$ over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp-Massey(B-M) algorithm and the rational approximation algorithm(RAA), these sequences have quite good cryptographyic properties in the aspect of linear complexity and 2-adic complexity.
The generalized cyclotomic binary sequences $S=S(a, b, c)$ with period $n=pq$ have good autocorrelation property where $(a, b, c)in {0, 1}^3$ and $p, q$ are distinct odd primes. For some cases, the sequences $S$ have ideal or optimal autocorrelation.
Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequences of period $4p$ with optimal autocorrelation magnitude was constructed in cite{W. Su}. Later, Fan showed that the linear complexity of this class of sequences is quite good cit
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in [1] and [3].
In cryptography, we hope a sequence over $mathbb{Z}_m$ with period $N$ having larger $m$-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In this paper,
In this paper, we determine the 4-adic complexity of the balanced quaternary sequences of period $2p$ and $2(2^n-1)$ with ideal autocorrelation defined by Kim et al. (ISIT, pp. 282-285, 2009) and Jang et al. (ISIT, pp. 278-281, 2009), respectively. O