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

Document Type

Article

Publication Date

2-2007

Department

Department of Mathematical Sciences

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.

Publication Title

Designs, Codes, and Cryptography

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