Work

On subspace designs

Year: 2023

Type: article

Abstract: Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we provide bounds involving the parameters of a subspace design, showing they are tight via explicit constructions. We point out a connection with sum-rank metric codes, dealing with optimal codes and minimal codes with respect to this metric. Applications to two-intersection sets with respect to hyperplanes, two-weight codes, cutting blocking sets and lossless dimension expanders are also provided.

Source: EMS Surveys in Mathematical Sciences

DOI: 10.4171/emss/77

Authors: Paolo Santonastaso, Ferdinando Zullo

Institution: University of Campania "Luigi Vanvitelli"

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

OpenAlex ID: W4225086716

FWCI: 1.071

Cites:

Cited by: 12

Related to: 10