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Hadamard Conjecture Proof

EasyChair Preprint no. 8250

3 pagesDate: June 12, 2022


The most important open question in the theory of Hadamard matrices is that of existence (the Hadamard conjecture). The generalization of Sylvester’s construction proves that if H_n and H_m are Hadamard matrices of orders n and m, respectively, then H_n x H_m given by the Kronecker product is a Hadamard matrix of order nm. This result is used to produce Hadamard matrices of higher order once those of smaller orders are known.

Here we go in the opposite direction: we show how to construct a Hadamard matrix of order 4n from a Hadamard matrix of order 4nm. The outcome gives the link to Number Theory with a way to prove the Hadamard conjecture, using Paley’s work.

Keyphrases: coding theory, discrete Fourier analysis, Hadamard codes, Hadamard conjecture, Hadamard matrix, integer lattices, Kronecker product, Paley’s work

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Valerii Sopin},
  title = {Hadamard Conjecture Proof},
  howpublished = {EasyChair Preprint no. 8250},

  year = {EasyChair, 2022}}
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