Another Generalization of the Reed-Muller Codes
Cunsheng Ding, Chunlei Li, and Yongbo Xia
TL;DR
This paper introduces a new generalization of punctured binary Reed-Muller codes and constructs related reversible cyclic codes, expanding the theoretical framework of coding theory.
Contribution
It presents a novel generalization of punctured binary Reed-Muller codes and constructs a related family of reversible cyclic codes, enhancing existing code structures.
Findings
New generalization of punctured binary Reed-Muller codes
Construction of reversible cyclic codes related to the new generalization
Theoretical expansion of coding code families
Abstract
The punctured binary Reed-Muller code is cyclic and was generalized into the punctured generalized Reed-Muller code over in the literature. The major objective of this paper is to present another generalization of the punctured binary Reed-Muller code. Another objective is to construct a family of reversible cyclic codes that are related to the newly generalized Reed-Muller codes.
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Taxonomy
TopicsCoding theory and cryptography · DNA and Biological Computing · Cellular Automata and Applications