The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation

Abstract

Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of sequence with three-level autocorrelation and analyze the 2-adic complexity of this sequence. Our results show that the 2-adic complexity of the sequence is at least (N + 1) − log 2 (N + 1) and that in many cases it is maximal, which is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude

“…In order to derive a lower bound on the 2-adic complexity of Yu-Gong sequence, we need employ the method of Hu [5]. It can be described as the following Lemma 1, which have also been used in several other references [15,4,10,11].…”

“…In this paper, the method of Hu [9] will be employed to analyze the 2-adic complexity of s and it can be described as the following Lemma 3 which has also been used in our another work [15].…”

2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

“…Hu [6] subsequently provided a simpler way which depends on the autocorrelation function to show that the 2-adic complexity of ideal 2-level autocorrelation sequences achieves the maximum. Thereafter, their methods were applied to compute the 2-adic complexities of several classes of sequences with optimal autocorrelation value [7,14,19,20] and some generalized cyclotomic sequences [13,21]. Very recently, Zhang et al [24] determined the 2-adic complexity of Ding-Helleseth-Martinsen sequences by using specifically defined "Gauss periods" and "quadratic Gauss sums".…”

Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of p-Ary m-Sequence

“…Recently, Zhang et al introduced a new method to determine the 2-adic complexity of a binary sequence by "Gauss periods" and "Gauss sum" over a ring Z N of residue classes modulo an integer N [29]. More applications of these three methods can be found in [11], [18]- [20], [24], [28], in which the 2-adic complexity of Legendre sequences, Jacobi sequences, modified Jacobi sequences and a class of binary sequences with optimal autocorrelation was analyzed.…”