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Polynomial Invariant Theory and Shape Enumerator of Self-Dual Codes in the NRT-Metric.
- Source :
- IEEE Transactions on Information Theory; Jul2020, Vol. 66 Issue 7, p4061-4074, 14p
- Publication Year :
- 2020
-
Abstract
- 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 $ {M}_{ {n},2}(\mathbb {F}_{2})$. 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 $ {M}_{ {n}, {s}}(\mathbb {F}_{2})$. We define the ordered flip of a matrix $ {A}\in {M}_{ {k},{ { ns}}}(\mathbb {F}_{ {q}})$ and present some constructions of self-dual NRT codes over $\mathbb {F}_{ {q}}$. We further give an application of ordered flip to the classification of self-dual NRT codes of dimension two. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
CIPHERS
LINEAR codes
GEOMETRIC shapes
METRIC spaces
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 144242895
- Full Text :
- https://doi.org/10.1109/TIT.2020.2971989