4 papers
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…
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…
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…
Structure theorem of square complex orthogonal design
Yuan Li
Square COD (complex orthogonal design) with size is an matrix , where each entry is a complex linear combination of and their conjugat…