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September 19, 2025Journal of Physics Conference SeriesOpen Access

Decreasing Monomial Codes over the Quaternary Ring ℤ4

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Authors

KSKeneth Joshua P. SardanVSVirgilio P. Sıson

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Overview

This research demonstrates a systematic method for generating quaternary monomial codes, implying a new framework for Reed-Muller codes.

Key Points

  • The study characterizes quaternary Reed-Muller codes as decreasing monomial codes using an algebraic framework.
  • Decreasing monomial codes are constructed by evaluating over the ring ℤ 4, determining minimal generating sets.
  • The results confirm that several generated codes meet known upper bounds, showcasing the effectiveness of this method.
  • Evaluations based on a refined partial order on monomials are key to optimizing code generation in this research.

Cite This Study

Sardan et al. (2025) studied this question.

synapsesocial.com/papers/68d466be31b076d99fa65b18https://doi.org/10.1088/1742-6596/3114/1/012013
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