2019/04/08 by Welington Santos, Santos, Welington, Marcelo Muniz S. Alves +2
Computer Science · Engineering · Mathematics · #11T71 #13A50 #68P30 #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT #msc:11T71 #msc:13A50 #msc:68P30
paper · pdf · doi:10.48550/arxiv.1904.04333
arxiv created 2019/04/08 · openalex publication_date 2019/04/08 · arxiv updated 2019/04/10 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
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⊆ Mn,2(\mathbbF2). 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 Mn,s(\mathbbF2). We define the ordered flip of a matrix A∈ Mk,ns(\mathbbFq) and present some constructions of self-dual NRT-codes over \mathbbFq. We further give an application of ordered flip to the classification of bidimensional self-dual NRT-codes.