MacWilliams duality for rank metric codes over finite chain rings
Iv\'an Blanco-Chac\'on, Alberto F. Boix, Marcus Greferath, Erik, Hieta-aho
TL;DR
This paper extends MacWilliams duality theory to rank metric codes over finite chain rings, establishing a relationship between the q-binomial moments of a code and its dual, thus broadening the theoretical framework for such codes.
Contribution
It generalizes Ravagnani's MacWilliams duality to finite chain rings, linking the moments of a code and its dual in the rank metric setting.
Findings
Established duality relations for rank metric codes over finite chain rings.
Connected q-binomial moments of codes with their duals.
Extended the theoretical understanding of rank metric codes in algebraic structures.
Abstract
We extend Ravagnani's MacWilliams duality theory to the settings of rank metric codes over finite chain rings, relating the sequences of -binomial moments of a rank metric code over this class of rings with those of its dual.
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Taxonomy
TopicsRings, Modules, and Algebras · Coding theory and cryptography · graph theory and CDMA systems