Generalized Reed-Muller codes over Galois rings
Harinaivo Andriatahiny, Desir\'e Ars\`ene Ratahirinjatovo, Sanni, Jos\'e Andrianalisefa
TL;DR
This paper extends the concept of Generalized Reed-Muller codes from prime power residue rings to Galois rings, broadening their algebraic framework and potential applications.
Contribution
It introduces a new generalization of Reed-Muller codes over Galois rings, expanding the algebraic structures used in coding theory.
Findings
Established the construction of Reed-Muller codes over Galois rings.
Analyzed properties and potential advantages of these codes.
Provided foundational results for further research in coding over Galois rings.
Abstract
Recently, Bhaintwal and Wasan studied the Generalized Reed-Muller codes over the prime power integer residue ring. In this paper, we give a generalization of these codes to Generalized Reed-Muller codes over Galois rings.
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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Educational Curriculum and Learning Methods