One Note About the Tu-Deng Conjecture in Case $\mathop{\mathrm{w}} olimits(t)=5$
Yindong Chen, Fei Guo, Zhangquan Gong, Weihong Cai · IEEE Access · 2019
Let k ≥ 2 be an integer, and define St:= {(a, b) ∈ Z2|0 ≤ a, b ≤ 2k - 2, a + b = t(mod 2k- 1), w(a) + w(b) ≤ k - 1}, where t ∈ Z, 1 ≤ t ≤ 2k- 2. This paper gives the upper bound of the cardinality of Stin 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.