Abstract: Error Correcting Output Codes (ECOC) represent a successful framework to deal with multi-class categorization problems based on combining binary classifiers. In this paper, we present a new formulation of the ternary ECOC distance and the error-correcting capabilities in the ternary ECOC framework. Based on the new measure, we stress on how to design coding matrices preventing codification ambiguity and propose a new Sparse Random coding matrix with ternary distance maximization. The results on the UCI Repository and in a real speed traffic categorization problem show that when the coding design satisfies the new ternary measures, significant performance improvement is obtained independently of the decoding strategy applied.