Dual skew codes from annihilators: Transpose Hamming ring extensions
Jos\'e G\'omez-Torrecillas, F. J. Lobillo, Gabriel Navarro
TL;DR
This paper introduces a framework for analyzing the duals of skew cyclic codes using transposed Hamming ring extensions, demonstrating that duals of various skew codes remain within the same class.
Contribution
It proposes a novel algebraic framework based on anti-isomorphisms for studying duals of skew cyclic codes, extending to several classes of skew codes.
Findings
Duals of skew cyclic codes belong to the same class
Framework applies to convolutional, constacyclic, and Reed-Solomon skew codes
Dual codes preserve structural properties
Abstract
In this paper a framework to study the dual of skew cyclic codes is proposed. The transposed Hamming ring extensions are based in the existence of an anti-isomorphism of algebras between skew polynomial rings. Our construction is applied to left ideal convolutional codes, skew constacyclic codes and skew Reed-Solomon code, showing that the dual of these codes belong to the same class.
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