chapter  Chapter 4
10 Pages

Singleton bound and Reed-Solomon codes

ByJuergen Bierbrauer

Matrices of the type that obtain as generator matrices of Reed-Solomon codes are known as Vandermonde matrices. It is clear now how to determine the minimum distance of Reed-Solomon codes in general. The number of roots of a nonzero polynomial of degree < k is = k- 1. The strength of the Reed-Solomon codes is as large as it could possibly be. Readers who know Lagrange interpolation will realize this right away. In general we concentrate on linear codes as they are easier to construct and to work with. However, there are a number of situations when very good nonlinear codes can be constructed. Most diverse methods are being used for the construction of covering arrays, from combinatorial design theory and coding theory to heuristic search methods. Various names are employed, from qualitatively independent partitions to t-independentsets and universal sets.