Polynomial Invariant Theory and Shape Enumerator of Self-Dual Codes in the NRT-Metric

04/08/2019

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by   Welington Santos, et al.

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In this paper we consider self-dual NRT-codes, that is, self-dual codes in the metric space endowed with the Niederreiter-Rosenbloom-Tsfasman (NRT-metric). We use polynomial invariant theory to describe the shape enumerator of a binary self-dual, doubly even self-dual, and doubly-doubly even self dual NRT-code C⊆ M_n,2(F_2). Motivated by these results we describe the number of invariant polinomials that we must find to describe the shape enumerator of a self-dual NRT-code of M_n,s(F_2). We define the ordered flip of a matrix A∈ M_k,ns(F_q) and present some constructions of self-dual NRT-codes over F_q. We further give an application of ordered flip to the classification of bidimensional self-dual NRT-codes.