6 papers
Minimal Ternary Linear Codes from Vectorial Functions
Yanjun Li, Haibin Kan, Fangfang Liu +3
The study on minimal linear codes has received great attention due to their significant applications in secret sharing schemes and secure two-party computation. Until now, numerous…
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…
Characterization for a generic construction of bent functions and its consequences
Yanjun Li, Jinjie Gao, Haibin Kan +3
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions…
On the Uniqueness of Balanced Complex Orthogonal Design
Yiwen Gao, Yuan Li, Haibin Kan
Complex orthogonal designs (CODs) play a crucial role in the construction of space-time block codes. Their real analog, real orthogonal designs (or equivalently, sum of squares com…
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…
The Covering Radius of the Third-Order Reed-Muller Code RM(3,7) is 20
Jinjie Gao, Haibin Kan, Yuan Li +1
We prove the covering radius of the third-order Reed-Muller code RM(3,7) is 20, which was previously known to be between 20 and 23 (inclusive). The covering radius of RM(3, 7) is t…