---
title: On the structure of generalized toric codes
url: https://www.emergentmind.com/papers/0611010
type: paper
arxiv_id: '0611010'
arxiv_url: https://arxiv.org/abs/0611010
published: '2006-11-02'
categories:
- cs.IT
- math.IT
---

# On the structure of generalized toric codes

## Abstract

Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so called generalized toric codes. This extension consists on evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance.