---
title: Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes
url: https://www.emergentmind.com/papers/0703104
type: paper
arxiv_id: '0703104'
arxiv_url: https://arxiv.org/abs/0703104
published: '2007-03-22'
categories:
- cs.IT
- math.IT
---

# Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes

## Abstract

We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gr\"obner basis of the locator ideal for a set of rational points and the two-dimensional inverse discrete Fourier transform. We generalize the functioning of the generator polynomial for Reed-Solomon codes and develop systematic encoding for various algebraic codes.