Gr\"obner Bases for Linearized Polynomials
Margreta Kuijper, Anna-Lena Trautmann
TL;DR
This paper develops a new theoretical framework for Gr"obner bases specifically tailored to modules over the ring of univariate linearized polynomials with finite field coefficients, expanding algebraic tools in this domain.
Contribution
It introduces the theory of Gr"obner bases for modules over the ring of univariate linearized polynomials, a novel extension in algebraic computation.
Findings
Established foundational properties of Gr"obner bases in this context
Provided algorithms for computing these bases
Enhanced algebraic methods for finite field modules
Abstract
In this work we develop the theory of Gr\"obner bases for modules over the ring of univariate linearized polynomials with coefficients from a finite field.
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · Algebraic Geometry and Number Theory