On Fourier and Hadamard matrices of prime order
Year: 2026
Type: preprint
Abstract: We study how much of the Fourier matrix of prime order is needed to recognize it among regular or Butson Hadamard matrices. For every odd prime, the block whose rows and columns are indexed by the nonzero squares determines the Fourier matrix up to equivalence. We also prove an entrywise power dichotomy and obtain a recognition criterion from a two-orbit symmetry at every odd prime through 109. The repository contains the paper, its LaTeX source, and the Python and C++ programs, inputs, and certificates for the finite calculations. ChatGPT assisted with developing mathematical arguments, drafting the manuscript, and writing and checking the computational code. The paper carries the byline Teo B and Chat GPT.
Authors: Banica, Teodor, GPT, Chat
Institution: CY Cergy Paris Université
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225598149