Two-dimensional Burst Error Correcting Code using Finite Field Fourier Transforms

TL;DR

This paper introduces a novel two-dimensional burst error correcting code leveraging finite field Fourier transforms, enabling efficient correction of multiple error patterns in data storage and barcode applications.

Contribution

It presents a new code construction method using finite field Fourier transforms for two-dimensional burst error correction, with encoding and decoding in the transformed domain.

Findings

Capable of correcting multiple non-overlapping error patterns

Efficient encoding and decoding in the Fourier transform domain

Applicable to data storage and barcode systems

Abstract

We construct two-dimensional codes for correcting burst errors using the finite field Fourier transform. The encoding procedure is performed in the transformed domain using the conjugacy property of the finite field Fourier transform. The decoding procedure is also done in the transformed domain. Our code is capable of correcting multiple non-overlapping occurrence of different error patterns from a finite set of predefined error patterns. The code construction is useful for encoding data in two dimensions for application in data storage and bar codes