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

Carla Mascia; Giancarlo Rinaldo; Massimiliano Sala

doi:10.3934/amc.2018018

Article Contents

2018, Volume 12, Issue 2: 287-301. Doi: 10.3934/amc.2018018

This issue Previous Article Indiscreet logarithms in finite fields of small characteristic Next Article Several infinite families of p-ary weakly regular bent functions

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

Università degli Studi di Trento, Trento, Italy

Received: September 30, 2016

Revised: October 31, 2017

Published: April 2018

This research was partially funded by the Italian Ministry of Education, Universities and Research, with the project PRIN 2015TW9LSR "Group theory and applications"

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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.

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Mathematics Subject Classification: Primary: 13P25, 11T71; Secondary: 12Y05.

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