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

Abstract

In 2008, a class of binary sequences of period N = 4(2 k − 1)(2 k + 1) with optimal autocorrelation magnitude has been presented by Yu and Gong based on an m-sequence, the perfect sequence (0, 1, 1, 1) of period 4 and interleaving technique. In this paper, we study the 2-adic complexities of these sequences. Our results show that they are larger than N − 2⌈log 2 N ⌉ (which is far larger than N/2) and could attain the maximum value N if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.

On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences

“…Particularly, H. Hu [5] presented a neat approach to show that for all known ideal binary sequences with period N, their 2-adic complexity reaches the maximum value log 2 (2 N − 1). For some other sequences with good autocorrelation, the 2-adic complexity is determined or estimated by a nice lower bound [4,[9][10][11]13].…”

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

“…Case 1. k = 1, 3. In this case, we get from Lemma 11 and congruences in (15), (1) + N (mod m). When b(1) = 0, we get m = N and hence 2 N ≡ −1 (mod N).…”

“…Moreover, Su et al [12] presented a construction of binary sequences of period 4p via interleaving four suitable Ding-Helleseth-Lam sequences. Very recently, the linear complexity and 2-adic complexity of these sequences were determined respectively in [4] and [15,22].…”

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

“…We only present the proof for the case of p ≡ 3 (mod 4) and the other case is similar. Substituting (20) in Theorem 1 into (23) in Lemma 4, we have…”

“…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.…”