Accueil

Dion C. Gijswijt

  1. Invariant semidefinite programs.

    Tue, 07/20/2010 - 15:01 — SomNambul
    Authors: Christine Bachoc, Frank Vallentin, Dion C. Gijswijt, Alexander Schrijver
    Subjects: Optimization and Control
    Abstract

    In the last years many results in the area of semidefinite programming were
    obtained for invariant (finite dimensional, or infinite dimensional)
    semidefinite programs - SDPs which have symmetry. This was done for a variety
    of problems and applications. The purpose of this handbook chapter is to give
    the reader the necessary background for dealing with semidefinite programs
    which have symmetry. Here the basic theory is given and it is illustrated in
    applications from coding theory, combinatorics, geometry, and polynomial
    optimization.

  2. Semidefinite code bounds based on quadruple distances.

    Fri, 05/28/2010 - 15:01 — SomNambul
    Authors: Dion C. Gijswijt, Hans D. Mittelmann, Alexander Schrijver
    Subjects: Combinatorics
    Abstract

    Let $A(n,d)$ be the maximum number of $0,1$ words of length $n$, any two
    having Hamming distance at least $d$. We prove $A(20,8)=256$, which implies
    that the quadruply shortened Golay code is optimal. Moreover, we show
    $A(18,6)\leq 673$, $A(19,6)\leq 1237$, $A(20,6)\leq 2279$, $A(23,6)\leq 13674$,
    $A(19,8)\leq 135$, $A(25,8)\leq 5421$, $A(26,8)\leq 9275$, $A(21,10)\leq 47$,
    $A(22,10)\leq 84$, $A(24,10)\leq 268$, $A(25,10)\leq 466$, $A(26,10)\leq 836$,
    $A(27,10)\leq 1585$, $A(25,12)\leq 55$, and $A(26,12)\leq 96$.

Math-arch

Syndicate content