Hilbert quasi-polynomial for order domains and application to coding theory

TL;DR

This paper introduces a novel application of Hilbert quasi-polynomials to order domains, enabling more efficient verification of their properties and improving the identification of order domain codes in coding theory.

Contribution

It presents a new method using Hilbert quasi-polynomials for order domain analysis and an improved algorithm for their computation, facilitating code identification.

Findings

Effective check of second order-domain condition achieved

Enhanced algorithm for Hilbert quasi-polynomial computation

Simplified identification of order domain codes

Abstract

We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert quasi-polynomials. This allows to identify order domain codes more easily.