Decoding of Space-Symmetric Rank Errors

TL;DR

This paper explores decoding Gabidulin codes over channels with space-symmetric errors, demonstrating effective decoding of high-rank errors using specialized bases, which enhances error correction capabilities.

Contribution

It introduces a decoding method for Gabidulin codes tailored to space-symmetric errors, leveraging weak-self orthogonal bases for improved error correction.

Findings

Errors of rank up to 2(n-k)/3 can be decoded with high probability.

Decoding is effective using weak-self orthogonal bases.

The approach extends the decoding capability for specific error structures.

Abstract

This paper investigates the decoding of certain Gabidulin codes that were transmitted over a channel with space-symmetric errors. Space-symmetric errors are additive error matrices that have the property that their column and row spaces are equal. We show that for channels restricted to space-symmetric errors, with high probability errors of rank up to 2(n-k)/3 can be decoded with a Gabidulin code of length n and dimension k, using a weak-self orthogonal basis as code locators.