Codes Andn-ary Relations

Abstract

The aim of this thesis is to develop a general mechanism for the construction of codes and to extract general properties of classes of codes. This mechanism makes it unnecessary to study various classes of codes separately--at least to some extent--by different constructions and properties.;To achieve this goal, the mechanism of characterizing classes of languages by binary relations is studied. Some general properties related to binary relations and languages are obtained. Moreover, three new classes of codes, n-shuffle codes, solid codes, and intercodes are constructed. Solid codes and intercodes have the synchronous decoding property which is very useful in the design of circuits of coders and decoders.;The studies of codes, n-codes, and intercodes indicate that these three classes of codes cannot be characterized by binary relations. We introduce a more general mechanism, that is, to characterize classes of languages by finitary relations. This mechanism can be used to characterize more classes of languages, such as the classes of n-codes and intercodes. Sometimes, it is difficult to show inclusion relations between classes of codes and hierarchy properties of classes of codes. Results derived in this thesis provide a mechanism which can simplify this task