Duals of linearized Reed-Solomon codes
Xavier Caruso (IMB, LFANT), Amaury Durand (IMB, LFANT)
TL;DR
This paper characterizes the duals of linearized Reed-Solomon codes using residues of Ore rational functions, demonstrating their stability under duality under certain conditions, and develops a residue theory in the Ore setting.
Contribution
It introduces a novel description of dual codes via Ore rational functions and establishes their stability under duality, along with a new residue theory in Ore algebra.
Findings
Duals of linearized Reed-Solomon codes are described using Ore residues.
Under certain conditions, these codes are stable under duality.
A new residue theory in Ore algebra is developed.
Abstract
We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of linearized Reed-Solomon codes is stable under duality. As a byproduct of our work, we develop a theory of residues in the Ore setting.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Finite Group Theory Research