Results of Delsarte-Goethals on Sets of Matrices with Good Rank Properties
Speaker: Gary McGuire (UCD)
Date: Mon 31st March 2008
Location: Mathematical Sciences Seminar Room
In a 1975 paper, Delsarte and Goethals proved an upper bound on the size of a set of skew-symmetric matrices over a finite field having a good rank property. Here, by a good rank property we mean that the difference of any two matrices has rank at least 2d. We will present their proof of this bound, which uses association schemes, and discuss sets of matrices that meet the bound. Such sets of matrices have applications in network coding and spacetime coding.
(This talk is part of the Algebra/Claude Shannon Institute series.)