3 papers
cs.CR2023
Trace Monomial Boolean Functions with Large High-Order Nonlinearities
Jinjie Gao, Haibin Kan, Yuan Li +2
Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bo…
math.CO2023
A Gröbner Basis Approach to Combinatorial Nullstellensatz
Yang Xu, Haibin Kan, Guangyue Han
In this paper, using some conditions that arise naturally in Alon's combinatorial Nullstellensatz as well as its various extensions and generalizations, we characterize Gröbner bas…
cs.IT2022
Minimal Binary Linear Codes from Vectorial Boolean Functions
Yanjun Li, Jie Peng, Haibin Kan +1
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put fo…