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Mathematics > Combinatorics

arXiv:2511.14653 (math)
[Submitted on 18 Nov 2025]

Title:Asymptotically optimal approximate Hadamard matrices

Authors:Boris Alexeev, John Jasper, Dustin G. Mixon
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Hadamard matrices, by Boris Alexeev and 2 other authors
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    Abstract:In this paper, we study approximate Hadamard matrices,
    that is, well-conditioned $n\times n$ matrices with all entries
    in $\{\pm1\}$. We show that the smallest-possible condition
    number goes to $1$ as $n\to\infty$, and we identify some explicit
    infinite families of approximate Hadamard matrices.

Comments: See the ancillary files for putatively optimal matrices and
          Lean code
Subjects: Combinatorics (math.CO); Functional Analysis (math.FA)
Cite as:  arXiv:2511.14653 [math.CO]
          (or arXiv:2511.14653v1 [math.CO] for this version)
          https://doi.org/10.48550/arXiv.2511.14653
          Focus to learn more
          arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Dustin Mixon [view email]
[v1] Tue, 18 Nov 2025 16:47:55 UTC (18 KB)
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Ancillary-file links:

Ancillary files (details):

  * H03.txt
  * H05.txt
  * H06.txt
  * H07.txt
  * H09.txt

  * H10.txt
  * H11.txt
  * H13.txt
  * H14.txt
  * H15.txt
  * H17.txt
  * H18.txt
  * H19.txt
  * H21.txt
  * H22.txt
  * H23.txt
  * H25.txt
  * H26.txt
  * H27.txt
  * H29.txt
  * H30.txt
  * Orthogonal.lean

  * (17 additional files not shown) You must enabled JavaScript to
    view entire file list.

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