The minimal polynomials of modified de Bruijn sequences revisited

Wang, Hongyu; Zheng, Qun-Xiong; Wang, Zhongxiao; Qi, Wei

doi:10.1016/j.ffa.2020.101735

Cited by 4 publications

(15 citation statements)

References 12 publications

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“…The converse also holds. For any f (x) and g(x) in F 2 [x] satisfying (12), there exists a periodic sequence s for which (11) holds. The requirement that gcd(g(x), f (x)) = 1 is not strictly necessary.…”

Section: Preliminariesmentioning

confidence: 99%

“…while c / ∈ S or d / ∈ S do (1, 13), (13, 5), (5, 10), (10,11), (11,9), (9, 2), (2, 4), (4, 7), (7,14), (14, 3), (3,6), (6,12), (12,8), (8,15).…”

Section: Hamiltonian Cycles By Two Greedy Algorithmsmentioning

confidence: 99%

“…Example 5. A randomized instance for n = 4 picks Ψ = (6, 3, 9, 13, 5, 10, 11) • (4, 7, 1, 2) • (14,12,8,15).…”

Section: More Hamiltonian Cycles By Cycle Joiningmentioning

confidence: 99%

“…Example 7. Let H ∈ Γ 4 be given in terms of its successive vertices (1,13,5,10,11,9,2,4,7,14,3,6,12,8,15).…”

Section: The Canonical Generator Polynomialmentioning

confidence: 99%

“…An early work on this topic was done by Mayhew and Golomb in [9]. Subsequent works by Kyureghyan in [10], by Tan, Xu, and Qi in [11], and a more recent one by Wang, Cheng, Wang, and Qi in [12] have not managed to supply any systematic method to determine the minimal polynomials.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences

Musthofa¹,

Wijayanti²,

Palupi³

et al. 2022

Preprint

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A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique least-degree characteristic polynomial. Leveraging on a recent characterization, we devise a novel general approach to determine the minimal polynomial. We translate the characterization into a problem of identifying a Hamiltonian cycle in a specially constructed graph. Along the way, we demonstrate the usefullness of computational tools from the cycle joining method in the modified setup.

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Section: Preliminariesmentioning

confidence: 99%

“…while c / ∈ S or d / ∈ S do (1, 13), (13, 5), (5, 10), (10,11), (11,9), (9, 2), (2, 4), (4, 7), (7,14), (14, 3), (3,6), (6,12), (12,8), (8,15).…”

Section: Hamiltonian Cycles By Two Greedy Algorithmsmentioning

confidence: 99%

“…Example 5. A randomized instance for n = 4 picks Ψ = (6, 3, 9, 13, 5, 10, 11) • (4, 7, 1, 2) • (14,12,8,15).…”

Section: More Hamiltonian Cycles By Cycle Joiningmentioning

confidence: 99%

“…Example 7. Let H ∈ Γ 4 be given in terms of its successive vertices (1,13,5,10,11,9,2,4,7,14,3,6,12,8,15).…”

Section: The Canonical Generator Polynomialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences

Musthofa¹,

Wijayanti²,

Palupi³

et al. 2022

Preprint

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Introduction

Etzion

2024

Sequences and the De Bruijn Graph

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A Survey on Complexity Measures for Pseudo-Random Sequences

2024

Cryptography

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Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements on the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical computer science and of practical interest in cryptography. This survey reviews notable research from the past four decades on the linear, quadratic and maximum-order complexities of pseudo-random sequences, and their relations with Lempel–Ziv complexity, expansion complexity, 2-adic complexity and correlation measures.

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The minimal polynomials of modified de Bruijn sequences revisited

Cited by 4 publications

References 12 publications

A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences

A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences

Introduction

A Survey on Complexity Measures for Pseudo-Random Sequences

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