A remark on ๐”ฝ_q^n-Linear MRD codes

by   Luca Giuzzi, et al.

In this note, we provide a description of the elements of minimum rank of a generalized Gabidulin code in terms of Grassmann coordinates. As a consequence, a characterization of linearized polynomials of rank at most n-k is obtained, as well as parametric equations for MRD-codes of distance d=n-k+1.



There are no comments yet.


page 1

page 2

page 3

page 4

โˆ™ 01/20/2022

Non-minimum tensor rank Gabidulin codes

The tensor rank of some Gabidulin codes of small dimension is investigat...
โˆ™ 10/05/2018

A note on spanoid rank

We construct a spanoid S on n elements with rank(S) > n^c f-rank(S) wher...
โˆ™ 01/28/2017

Efficient Rank Aggregation via Lehmer Codes

We propose a novel rank aggregation method based on converting permutati...
โˆ™ 10/15/2021

Linear maximum rank distance codes of exceptional type

Scattered polynomials of a given index over finite fields are intriguing...
โˆ™ 05/18/2018

Affine Cartesian codes with complementary duals

A linear code C with the property that C โˆฉ C^ = {0 } is said to be a lin...
โˆ™ 05/31/2021

Sum-rank product codes and bounds on the minimum distance

The tensor product of one code endowed with the Hamming metric and one e...
โˆ™ 06/13/2019

Characteristic Power Series of Graph Limits

In this note, we show how to obtain a "characteristic power series" of g...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.