3 papers
cs.IT2026
The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116
Yueying Lou, Youle Xu, Qichun Wang
Does there exist an 8-variable balanced Boolean function with nonlinearity 118? This is a famous and long-standing open problem in Boolean functions. In this paper, we give a negat…
cs.IT2026
The Covering Radius of the Reed--Muller Code RM(1,9) is 242
Qichun Wang, Yueying Lou, Zifan Wang
What is the covering radius of the Reed--Muller code RM(1,9) ? This is a long-standing open problem in cryptography and coding theory. In this paper, we resolve this problem, and p…
cs.IT2024
Determining the Weight Spectrum of the Reed--Muller Codes RM(m-6,m)
Yueying Lou, Qichun Wang
The weight spectra of the Reed-Muller codes were unknown for . In IEEE Trans. Inform. Theory 2024, Carlet determined the weight spectrum of for $…