Non-minimum tensor rank Gabidulin codes
Information Theory
2022-01-21 v1 Combinatorics
math.IT
Abstract
The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an -dimensional -linear generalized Gabidulin code in . This shows that such a code is never minimum tensor rank. In this way, we detect the first infinite family of Gabidulin codes which are not minimum tensor rank.
Keywords
Cite
@article{arxiv.2201.08242,
title = {Non-minimum tensor rank Gabidulin codes},
author = {Daniele Bartoli and Giovanni Zini and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2201.08242},
year = {2022}
}