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Designs, Codes and Cryptography

, Volume 42, Issue 2, pp 127–143 | Cite as

A direct approach to linear programming bounds for codes and tms-nets

  • Jürgen BierbrauerEmail author
Article

Abstract

Based on a self-contained account of the classical linear programming bounds for codes and orthogonal arrays we give a simplified description of the linear programming bounds for ordered codes, ordered orthogonal arrays (OOA) and tms-nets. The main result is a description in terms of a family of polynomials which generalize the Kravchouk polynomials of coding theory. The Plotkin bound and the sphere packing bound for ordered codes are consequences. We also derive a quadratic bound and illustrate by giving some improvements for bounds on the parameters of tms-nets.

Keywords

Linear programming bounds Codes Orthogonal arrays tms-nets Ordered orthogonal arrays Kravchouk polynomial Duality Plotkin bound Rao bound Lloyd polynomial 

AMS Classifications

11K38 11K45 94B65 05E30 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA

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