Low-Rank Matrix Recovery using Gabidulin Codes in Characteristic Zero

TL;DR

This paper introduces a novel method for low-rank matrix recovery over infinite fields by leveraging Gabidulin codes generalized to characteristic zero, enabling decoding-based solutions.

Contribution

It extends Gabidulin codes to characteristic zero fields and demonstrates their application in low-rank matrix recovery, bridging coding theory and matrix completion.

Findings

LRMR can be reduced to Gabidulin code decoding

Applicable to matrices over infinite fields

Guidelines for field extension choices

Abstract

We present a new approach on low-rank matrix recovery (LRMR) based on Gabidulin Codes. Since most applications of LRMR deal with matrices over infinite fields, we use the recently introduced generalization of Gabidulin codes to fields of characterstic zero. We show that LRMR can be reduced to decoding of Gabidulin codes and discuss which field extensions can be used in the code construction.