Graver Bases and Universal Gr\"obner Bases for Linear Codes
Natalia D\"uck, Karl-Heinz Zimmermann
TL;DR
This paper develops algorithms to compute Graver bases and universal Gr"obner bases for binomial ideals associated with linear codes, establishing a connection with toric ideals to enhance algebraic understanding.
Contribution
It introduces algorithms for computing Graver bases and universal Gr"obner bases of binomial ideals linked to linear codes, connecting these ideals with toric ideals.
Findings
Algorithms for Graver bases computation
Algorithms for universal Gr"obner bases computation
Connection established between binomial ideals and toric ideals
Abstract
Two correspondences have been provided that associate any linear code over a finite field with a binomial ideal. In this paper, algorithms for computing their Graver bases and universal Gr\"obner bases are given. To this end, a connection between these binomial ideals and toric ideals will be established.
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · Cryptography and Residue Arithmetic