A decoding algorithm for binary linear codes using Groebner bases
Harinaivo Andriatahiny, Jean Jacques Ferdinand Randriamiarampanahy,, Toussaint Joseph Rabeherimanana
TL;DR
This paper introduces a decoding algorithm for binary linear codes that leverages Groebner bases of associated binomial ideals, bridging coding theory with algebraic geometry techniques.
Contribution
It presents a novel decoding method for binary linear codes using Groebner bases, connecting algebraic geometry with coding theory.
Findings
Decoding algorithm effectively uses Groebner bases
Provides algebraic framework for binary code decoding
Enhances understanding of code structure through algebraic methods
Abstract
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear codes by utilizing the Groebner bases of the associated ideals.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Coding theory and cryptography