DeepAI AI Chat
Log In Sign Up

Divisible linear rank metric codes

11/15/2022
∙
by   Olga Polverino, et al.
∙
University College Dublin
∙
0
∙

A subspace of matrices over 𝔽_q^e^m× n can be naturally embedded as a subspace of matrices in 𝔽_q^em× en with the property that the rank of any of its matrix is a multiple of e. It is quite natural to ask whether or not all subspaces of matrices with such a property arise from a subspace of matrices over a larger field. In this paper we explore this question, which corresponds to studying divisible codes in the rank metric. We determine some cases for which this question holds true, and describe counterexamples by constructing subspaces with this property which do not arise from a subspace of matrices over a larger field.

READ FULL TEXT

page 1

page 2

page 3

page 4

∙ 06/01/2018

An Assmus-Mattson Theorem for Rank Metric Codes

A t-(n,d,λ) design over F_q, or a subspace design, is a collection of d...
∙ 03/04/2020

Degenerate flag varieties in network coding

Building upon the application of flags to network coding introduced by L...
∙ 04/27/2022

On subspace designs

The aim of this paper is to investigate the theory of subspace designs, ...
∙ 11/18/2021

On the Existence of Coproducts in Categories of q-Matroids

q-Matroids form the q-analogue of classical matroids. In this paper we i...
∙ 09/25/2019

Context-Aware Decentralized Invariant Signaling for Opportunistic Communications

A novel scenario-adapted distributed signaling technique in the context ...
∙ 05/17/2018

Systematic encoders for generalized Gabidulin codes and the q-analogue of Cauchy matrices

We characterize the generator matrix in standard form of generalized Gab...
∙ 02/24/2021

Binary Subspace Chirps

We describe in details the interplay between binary symplectic geometry ...