Decoding binary Reed-Muller codes via Groebner bases
Harinaivo Andriatahiny, Jean Jacques Ferdinand Randriamiarampanahy,, Toussaint Joseph Rabeherimanana
TL;DR
This paper presents a novel decoding method for binary Reed-Muller codes using Groebner bases, leveraging their algebraic structure for improved decoding efficiency.
Contribution
It introduces a new decoding approach for Reed-Muller codes based on Groebner bases, connecting algebraic properties with practical decoding techniques.
Findings
Successful decoding of Reed-Muller codes using Groebner bases
Demonstrates the algebraic structure aids in decoding efficiency
Provides a new perspective on code characterization
Abstract
The binary Reed-Muller codes can be characterized as the radical powers of a modular algebra. We use the Groebner bases to decode these codes.
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Taxonomy
TopicsCoding theory and cryptography · DNA and Biological Computing · graph theory and CDMA systems