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Asymptotically optimal approximate Hadamard matrices

2025/11/18 by Boris Alexeev, John Jasper, Alexeev, Boris +3 · 3 voices · 1 citation
Engineering · Mathematics · #graph theory and CDMA systems #Approximation Theory and Sequence Spaces #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2511.14653

Abstract

In this paper, we study approximate Hadamard matrices, that is, well-conditioned n× n matrices with all entries in \±1\. We show that the smallest-possible condition number goes to 1 as n→∞, and we identify some explicit infinite families of approximate Hadamard matrices.

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