A Lower Bound on the Constant in the Fourier Min-Entropy/Influence Conjecture

2022/12/15 by Aniruddha Biswas, Palash Sarkar, Biswas, Aniruddha +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2212.07713

Abstract

We describe a new construction of Boolean functions. A specific instance of our construction provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45 ≈ 2.8444 which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, 128/45 is also presently the best known lower bound on the universal constant of the Fourier min-entropy/influence conjecture.

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