Classification of Niederreiter–Rosenbloom–Tsfasman Block Codes

Poset and block metrics were introduced in recent years as alternative metrics to study error correcting codes. Poset-block codes were introduced in 2008, encompassing both poset and block metrics. In this paper, we study a family of such metrics, the Niederreiter-Rosenbloom-Tsfasman block metrics. In this context, we classify the classes of equivalent codes, describe canonical representatives of each class and develop much of the classical theory of error correcting codes for Niederreiter-Rosenbloom-Tsfasman block codes, including determination of packing radius and classification of MDS and perfect codes, determination of covering radius and characterization of quasi-perfect codes, and the description of an algorithm for syndrome decoding.