LDPC codes from Singer cycles

TL;DR

This paper explores the construction of LDPC codes using the orbits of subspaces in finite projective spaces under Singer cycle actions, aiming to improve error correction in communication systems.

Contribution

It introduces a novel approach to designing LDPC codes based on geometric group actions, expanding the methods for code construction in coding theory.

Findings

New LDPC code constructions from Singer cycle orbits

Potential for improved error correction performance

Enhanced understanding of geometric group actions in coding

Abstract

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes--characterised by admitting a sparse parity check matrix--with good correction capabilities. In the present paper the orbits of subspaces of a finite projective space under the action of a Singer cycle are investigated.