There exists a Hadamard matrix of order = , for all
A Hadamard matrix of order 428 (m=107) has been recently constructed .
A Hadamard matrix of order 764 has also recently been constructed .
Also, Paley’s theorem guarantees that there always exists a Hadamard matrix when is divisible by 4 and of the form , for some positive integers e and m, and p an odd prime and the matrices can be found using Paley construction.
This leaves the order of the lowest unknown Hadamard matrix as 668. There are 13 integers less than 500 for which no Hadamard matrix of order is known:
and all of them are primes congruent to 3 mod 4.
- 1 H. Kharaghani, B. Tayfeh-Rezaie, A Hadamard matrix of order 428, J. Comb. Designs 13, (2005), 435-440.
- 2 D.Z. Doković, Hadamard matrices of order 764 exist, http://arxiv.org/abs/math/0703312v1preprint.
|Date of creation||2013-03-22 14:07:07|
|Last modified on||2013-03-22 14:07:07|
|Last modified by||Mathprof (13753)|