The multiclass classification problem is considered and resolved through coding and regression. There are various coding schemes for transforming class labels into response scores. An equivalence notion of coding schemes is developed, and the regression approach is adopted for extracting a low-dimensional discriminant feature subspace. This feature subspace can be a linear subspace of the column span of original input data or kernel-mapped feature data. The classification training and prediction are carried out in this feature subspace using a linear classifier, which lead to a simple and computationally light but yet powerful toolkit for classification. Experimental results, including prediction ability and CPU time comparison with LIBSVM, show that the regression-based approach is a competent alternative for the multiclass problem.