New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes
Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala
TL;DR
This paper provides new algebraic descriptions of weighted and homogeneous Reed-Muller codes over prime and binary fields, along with a decoding method based on the Landrock-Manz approach.
Contribution
It introduces novel algebraic characterizations of these codes and develops a decoding procedure, enhancing understanding and potential decoding strategies.
Findings
Algebraic descriptions of weighted Reed-Muller codes over prime fields
Descriptions of homogeneous Reed-Muller codes in binary case
Decoding procedure using Landrock-Manz method
Abstract
We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. A description of the homogeneous Reed-Muller codes in the same ambient space is presented for the binary case. A decoding procedure using the Landrock-Manz method is developed.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · DNA and Biological Computing