Construction methods for multi-valued classification (multi-class) systems using binary classifiers are discussed and evaluated by a trade-off model for system evaluation based on rate-distortion theory. Suppose the multi-class systems consisted of M(≥3) categories and N(≥M-1) binary classifiers, then they can be represented by a matrix W, where the matrix W is given by a table of M code words with length N, called a code word table. For a document classification task, the relationship between the probability of classification error Pe and the number of binary classifiers N for given M is investigated, and we show that our constructed systems satisfy desirable properties such as “Flexible”, and “Elastic”. In particular, modified Reed Muller codes perform well: they are shown to be “Effective elastic”. As a second application we consider a hand-written character recognition task, and we show that the desirable properties are also satisfied.