Year: 2026
Type: preprint
Abstract: For sufficiently large $N$ which is a power of 2, we prove that changing at most one percent of the entries of the $N\times N$ Walsh-Hadamard Transform cannot reduce its rank over $\mathbb{F}_3$ to $\lfloor \log^2 N/80\rfloor$ or below. To the best of our knowledge, this is the first constant-fraction rigidity lower bound for an explicit matrix family at a superlogarithmic target rank over any choice of field, inching toward the parameters in Razborov's program for communication complexity lower bounds.
Source: arXiv (Cornell University)
Author: Alman, Josh
Institution: Columbia University
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7202121150
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