HADAMARD MATRICES


1./ New bounds for the number of Inequivalent Hadamard matrices of orders 44, 48, 52, 56, 60, 64, 68

Summary of the results:

Using Computational Algebra and High-performance Computing we computed explicitly sets of Inequivalent Hadamard matrices of orders 44, 48, 52, 56, 60, 64, 68, thus improving the lower bounds for the number of Inequivalent Hadamard matrices of orders 44, 48, 52, 56, 60, 64, 68.

  1. there are at least 500 inequivalent Hadamard matrices of order 44
  2. there are at least 55 inequivalent Hadamard matrices of order 48
  3. there are at least 638 inequivalent Hadamard matrices of order 52
  4. there are at least 205 inequivalent Hadamard matrices of order 56
  5. there are at least 256 inequivalent Hadamard matrices of order 60
  6. there are at least 395 inequivalent Hadamard matrices of order 64
  7. there are at least 340 inequivalent Hadamard matrices of order 68
Detailed presentation of the results:
Example of converting a Magma format file to a text file with the Hadamard matrices:
the Magma file order52ineq638.magma uses the Magma compact coding scheme for Hadamard matrices, available since Magma V2.11. To produce the text file order52ineq638.txt from the Magma file order52ineq638.magma, use the following Magma code: 
	        load "order52ineq638.magma";

	        n := #order52ineq638;
	        dime := 52;

	        for i in [1..n] do
		                print "matrix number",i;
		                HadamardMatrixFromInteger(order52ineq638[i],dime);
	        end for;


Acknowledgments:
  1. All computations in Magma have been performed remotely at the Centre de calcul formel MEDICIS, Ecole Polytechnique, Paris, France
  2. All computations in Maple have been performed at the Computer Algebra Research Group, CARGO, Wilfrid Laurier University, Waterloo, ON, Canada
  3. Computations in C have been performed remotely at SHARCnet high performance computing clusters, University of Western Ontario, London, ON, Canada
  4. Computations in C have been performed remotely at WestGrid high performance computing clusters, University of British Columbia, Simon Fraser University, Vancouver, BC, Canada

2./ Other Designs Systems and Tools
Page maintained by: Ilias S. Kotsireas
Last Update: October, 2004