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A compound error is any combination of burst errors with various burst lengths including random errors. The compound weight of any such error is defined as a kind of combinational metric which is a generalization of Gabidulin's metric. First, we present a fast method for calculating the weight of any word based on a kind of trellis diagram. Extending the two-dimensional trellis diagram to a three-dimensional trellis, we propose a method of constructing codes having higher coding rate by augmenting any compound-error-correcting codes. Furthermore, we propose a decoding method for any such codes by modifying the three-dimensional trellis in augmentation.