Association schemes and coding theory. (English) Zbl 0946.05086

Delsarte, Philippe; Levenshtein, Vladimir I.

IEEE Trans. Inf. Theory 44, No. 6, 2477-2504 (1998).

The authors present a detailed and comprehensive survey of association schemes and their applications to coding theory. The survey is concerned with a class of subjects that involve the central notion of distance distribution of a code. Special emphasis is put on the linear programming method. This produces upper bounds for the size of a code with a given minimum distance, and lower bounds for the size of a design with a given strength. The most specific results are obtained in the case where the underlying association scheme satisfies certain well-defined “polynomial properties.” In particular, some “universal bounds” are derived for codes and designs in polynomial type association schemes.

Reviewer: B.K.Dass (Delhi)

MSC:

05E30	Association schemes, strongly regular graphs
90C90	Applications of mathematical programming

Keywords:

codes and designs; duality; universal bounds; polynomial schemes; translation schemes; survey; association schemes; distance distribution; linear programming; upper bounds; lower bounds