On the 2-Adic Complexity of the Two-Prime Generator

“…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].…”

Section: The 2-adic Complexity Of Yu-gong Sequencementioning

confidence: 99%

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

et al. 2019

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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.

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“…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".…”

Section: Introductionmentioning

confidence: 99%

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

Xiao

Zeng

2021

Cryptogr. Commun.

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Three constructions of binary sequences with period 4N and optimal autocorrelation value or optimal autocorrelation magnitude have been presented by Tang and Gong based on interleaving technique. In this paper, the 2-adic complexity of the sequences with optimal autocorrelation magnitude constructed from the Legendre sequence pair or the twin-prime sequence pair is investigated. With the method proposed by Hu, we completely determine the 2-adic complexity of the sequences by calculating the exact autocorrelation distribution of the sequences and discussing the greatest common divisors. Results show that the 2-adic complexity of these sequences is either maximum or very close to maximum.

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On the 2-Adic Complexity of the Two-Prime Generator

Cited by 42 publications

References 13 publications

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

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

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

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

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