A new construction of anticode-optimal grassmannian codes

Issue Date

1-2021

Abstract

In this paper, we consider the well-known unital embedding from Fq k into Mk (Fq) seen as a map of vector spaces over Fq and apply this map in a linear block code of rate ρ/ℓ over Fq k. This natural extension gives rise to a rank-metric code with k rows, kℓ columns, dimension ρ and minimum distance k that satisfies the Singleton bound. Given a specific skeleton code, this rank-metric code can be seen as a Ferrers diagram rank-metric code by appending zeros on the left side so that it has length n − k. The generalized lift of this Ferrers diagram rank-metric code is a Grassmannian code. By taking the union of a family of the generalized lift of Ferrers diagram rank-metric codes, a Grassmannian code with length n, cardinalityqn −1, minimum injection distance k and dimension k that satisfies the qk −1 anticode upper bound can be constructed.

Source or Periodical Title

Journal of Algebra Combinatorics Discrete Structures and Applications

Volume

8

Issue

1

Page

33-41

Document Type

Article

Physical Description

figures

Language

English

Subject

Anticode bound, Constant dimension, Ferrers diagram, Grassmannian, Rank-metric code

Identifier

DOI:10.13069/jacodesmath.858732

Digital Copy

yes

En – AGROVOC descriptors

ANTICODE BOUND; CONSTANT DIMENSION; FERRERS DIAGRAM; GRASSMANIAN; RANK-METRIC CODE

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