Scalar products and Left LCD codes
Nabil Bennenni, Andr\'e Leroy
TL;DR
This paper introduces new scalar products over finite rings to define novel classes of left LCD codes, expanding the theoretical framework and providing conditions for their existence.
Contribution
It presents new scalar products over finite rings and defines left LCD codes with conditions for their existence, extending classical coding theory.
Findings
New scalar products over finite rings introduced
Definitions of right and left orthogonal codes established
Necessary and sufficient conditions for code existence provided
Abstract
In this article, we introduce new scalar products over finite rings via additive isomorphisms. This allows us to define new notions of right (respectively left) orthogonal codes, that are not necessarily linear. This leads to definitions of right (resp. left) dual codes and left LCD codes similar to the classical LCD codes. Furthermore, we provide necessary and sufficient conditions for the existence of these codes.
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Taxonomy
TopicsManufacturing Process and Optimization