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Horst Trinker1

  • 1Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria.

Discrete Mathematics
|April 17, 2012
PubMed
Summary
This summary is machine-generated.

This study generalizes semidefinite programming bounds for ordered codes and introduces a new linear programming bound for linear ordered codes. The research provides improved bounds for specific code parameters compared to existing methods.

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Area of Science:

  • Coding Theory
  • Discrete Mathematics
  • Information Theory

Background:

  • Semidefinite programming bounds, pioneered by Schrijver, leverage code triple distributions.
  • Ordered codes present unique challenges not fully addressed by existing bounds.

Purpose of the Study:

  • Generalize existing bounds for ordered codes.
  • Develop a new linear programming bound for linear ordered codes.
  • Identify parameters where the new bound outperforms standard methods.

Main Methods:

  • Generalization of semidefinite programming techniques for ordered codes.
  • Derivation of a MacWilliams-type identity for the triple distribution of dual codes.
  • Application of linear programming based on non-negativity constraints.

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Main Results:

  • A novel bound for ordered codes is established.
  • A MacWilliams-type identity for linear ordered codes is presented.
  • A linear programming bound is derived, outperforming standard bounds for specific parameters.

Conclusions:

  • The generalized approach provides tighter bounds for ordered codes.
  • The new linear programming bound offers enhanced performance for certain code parameters.
  • This work contributes to the advancement of coding theory bounds.