2019
DOI: 10.1109/access.2019.2894074
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One Note About the Tu-Deng Conjecture in Case <inline-formula> <tex-math notation="LaTeX">$\mathop{\mathrm{w}}\nolimits(t)=5$ </tex-math> </inline-formula>

Abstract: Let k ≥ 2 be an integer, and define S t := {(a, b) ∈ Z 2 |0 ≤ a, b ≤ 2 k − 2, a + b = t(mod 2 k − 1), w(a) + w(b) ≤ k − 1}, where t ∈ Z, 1 ≤ t ≤ 2 k − 2. This paper gives the upper bound of the cardinality of S t in the case of w(t) = 5. With this one, we conclude that a conjecture proposed by Tu and Deng in 2011 is right when w(t) = 5. INDEX TERMS Tu-Deng conjecture, algebraic immunity, Boolean function, Hamming weight.

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Cited by 8 publications
(2 citation statements)
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“…We also plan to further improve our model by considering the concept change n the traffic flow patterns, and further evaluate our model on other forecasting problems. Furthermore, the proposed model can be easily extended to other temporal related applications, such as multi-dimensional time series prediction [52], [53], prediction of stable bitstream [54], [55], recommendation systems [56] or temporal human emotion computing [57], etc.…”
Section: ) K-nearest Neighbor (Knn)mentioning
confidence: 99%
“…We also plan to further improve our model by considering the concept change n the traffic flow patterns, and further evaluate our model on other forecasting problems. Furthermore, the proposed model can be easily extended to other temporal related applications, such as multi-dimensional time series prediction [52], [53], prediction of stable bitstream [54], [55], recommendation systems [56] or temporal human emotion computing [57], etc.…”
Section: ) K-nearest Neighbor (Knn)mentioning
confidence: 99%
“…We do not explore the association between physical fitness and academic achievements among college students, which would be interesting. Our model is general, and can be extended other applications, such as traffic flow modeling [27]- [35], biomedical computing [36]- [38], intelligent computing [39]- [41] and algebraic immunity [42]- [45].…”
Section: Limitationsmentioning
confidence: 99%