Redundancies of Correction-Capability-Optimized Reed-Muller Codes
Maria Bras-Amor\'os, Michael E. O'Sullivan
TL;DR
This paper explores variations of Reed-Muller codes optimized for correction capability, providing explicit redundancy formulas to improve code rate while maintaining decoding performance with the Berlekamp-Massey-Sakata algorithm.
Contribution
Introduces new Reed-Muller code variations with explicit redundancy formulas that enhance rate without sacrificing decoding performance.
Findings
Redundancy formulas for the new code variants
Improved code rate for given decoding performance
Compatibility with Berlekamp-Massey-Sakata decoding
Abstract
This article is focused on some variations of Reed-Muller codes that yield improvements to the rate for a prescribed decoding performance under the Berlekamp-Massey-Sakata algorithm with majority voting. Explicit formulas for the redundancies of the new codes are given.
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Taxonomy
TopicsDNA and Biological Computing · Coding theory and cryptography · Error Correcting Code Techniques