Evaluation of iterated Ore polynomials and skew Reed-Muller codes
Andre Leroy, Nabil Bennenni
TL;DR
This paper investigates two methods for evaluating iterated Ore polynomials, compares their effectiveness, and uses these evaluations to construct and analyze skew Reed-Muller codes with explicit data.
Contribution
It introduces two evaluation techniques for iterated Ore polynomials and applies them to construct and analyze skew Reed-Muller codes, providing explicit data.
Findings
Comparison of evaluation methods for iterated Ore polynomials
Construction of Reed-Muller codes from these evaluations
Explicit data computed for the associated codes
Abstract
In this paper, we study two ways of evaluating iterated Ore polynomials. We provide many examples and compare these evaluations. We use the evaluation maps to construct Reed-Muller codes and compute explicitly some of the data that are associated to such codes.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Combinatorial Mathematics · Cellular Automata and Applications