Association schemes and coding theory. (English) Zbl 0946.05086

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)


05E30 Association schemes, strongly regular graphs
90C90 Applications of mathematical programming
Full Text: DOI