In this paper we consider self-dual NRT codes, that is, self-dual codes in the metric space endowed with the Niederreiter-Rosenbloom-Tsfasman metric (NRT metric) and their shape enumerators as defined by Barg and Park. We use polynomial invariant theory to describe the shape enumerator of a binary self-dual NRT code, even self-dual NRT code, and weak doubly even self-dual NRT code in Mn,2(F2). Motivated by these results, we describe the number of invariant polynomials that we must find to describe the shape enumerator of a self-dual NRT code in Mn,s(F2). We define the ordered flip of a matrix A ∈ Mk,ns(Fq) and present some constructions of self-dual NRT codes over Fq. We further give an application of ordered flip to the classification of self-dual NRT codes of dimension two.

In this note, we present an analogue for codes in vector spaces with a Rosenbloom-Tsfasman metric of the well-known standard form of generator matrices for codes in spaces with the Hamming metric.

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.