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

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Jürgen Bierbrauer

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  1. Jürgen Bierbrauer
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Correspondence to Jürgen Bierbrauer.

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Communicated by J. D. Key.

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Bierbrauer, J. A direct approach to linear programming bounds for codes and tms-nets. Des Codes Crypt 42, 127–143 (2007). https://doi.org/10.1007/s10623-006-9025-6

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  • DOI: https://doi.org/10.1007/s10623-006-9025-6

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