Matrix Algebras and Semidefinite Programming Techniques for Codes

Details Matrix Algebras and Semidefinite Programming Techniques for Codes Matrix Algebras and Semidefinite Programming Techniques for Codes

2010-07-06

arxiv.org/abs/1007.0906v1

Mathematics

Combinatorics

PhD Thesis (2005), about 100 pages

Scientific paper

This PhD thesis is concerned with SDP bounds for codes: upper bounds for (non)-binary error correcting codes and lower bounds for (non)-binary covering codes. The methods are based on the method of Schrijver that uses triple distances in stead of pairs as in the classical Delsarte bound. The main topics discussed are: 1) Block-diagonalisation of matrix *-algebras, 2) Terwilliger-algebra of the nonbinary Hamming scheme (including an explicit block-diagonalisation), 3) SDP-bounds for (nonbinary) error-correcting codes and covering codes (including computational results), 4) Discussion on the relation with matrix-cuts, 5) Computational results for Affine caps.

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