Generalized Reed-Muller codes over Galois rings

2018/01/16 by Harinaivo Andriatahiny, Andriatahiny, Harinaivo, Desiré Arsène Ratahirinjatovo +3
Computer Science · Mathematics · Social Sciences · #12E05 #94B05 #94B15 #Coding theory and cryptography #Educational Curriculum and Learning Methods #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication #cs.IT #math.IT #msc:12E05 #msc:94B05 #msc:94B15

paper · pdf · doi:10.48550/arxiv.1801.05114

arxiv created 2018/01/16 · openalex publication_date 2018/01/16 · arxiv updated 2018/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The Generalized Reed-Muller codes and the radical powers of a modular algebra
• The Generalized Reed-Muller codes in a modular group algebra
• New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes
• Another Generalization of the Reed-Muller Codes
• Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach