The geometry of Hermitian self-orthogonal codes

08/18/2021
βˆ™
by   Simeon Ball, et al.
βˆ™
0
βˆ™

We prove that if n >k^2 then a k-dimensional linear code of length n over 𝔽_q^2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than n common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
βˆ™ 01/08/2022

Self-orthogonal generalized twisted Reed-Solomon codes

In this paper, by calculating the dual code of the Schur square for the ...
research
βˆ™ 12/01/2020

Farthest sampling segmentation of triangulated surfaces

In this paper we introduce Farthest Sampling Segmentation (FSS), a new m...
research
βˆ™ 02/05/2020

Embedding linear codes into self-orthogonal codes and their optimal minimum distances

We obtain a characterization on self-orthogonality for a given binary li...
research
βˆ™ 06/18/2021

Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal

We prove that there is a Hermitian self-orthogonal k-dimensional truncat...
research
βˆ™ 08/30/2019

On numerical solution of full rank linear systems

Matrices can be augmented by adding additional columns such that a parti...
research
βˆ™ 11/24/2021

Self-orthogonality matrix and Reed-Muller code

Kim et al. (2021) gave a method to embed a given binary [n,k] code π’ž (k ...
research
βˆ™ 03/29/2023

Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

The purpose of this paper is two-fold. First, we characterize the existe...

Please sign up or login with your details

Forgot password? Click here to reset