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New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming

We give a new upper bound on the maximum size Aq (n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q ≥ 3 letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values of n and d. This work builds upon previous results of Schrijvcr [A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005) 2859-2866] on the Terwilliger algebra of the binary Hamming scheme.

Invariant Semidefinite Programs

This chapter provides the reader with the necessary background for dealing with semidefinite programs which have symmetry. The basic theory is given and it is illustrated in applications from coding theory, combinatorics, geometry, and polynomial optimization.

Approximation algorithms for hard capacitated k-facility location problems

We study the capacitated

Semidefinite Code Bounds Based on Quadruple Distances

k

Violating the Shannon capacity of metric graphs with entanglement

-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a constant number

Integer Decomposition for Polyhedra Defined by Nearly Totally Unimodular Matrices

k

ON THE b-STABLE SET POLYTOPE OF GRAPHS WITHOUT BAD K4 ∗

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On a packet scheduling problem for smart antennas and polyhedra defined by circular-ones matrices

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Clique partitioning of interval graphs with submodular costs on the cliques.

to open facility

Matrix algebras and semidefinite programming techniques for codes

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