A Singleton Bound for Generalized Ferrers Diagram Rank Metric Codes
Srikanth B. Pai, B. Sundar Rajan
TL;DR
This paper derives new upper bounds for generalized Ferrers diagram rank metric codes using classical Singleton bound techniques, extending existing bounds and introducing a broader class of codes.
Contribution
It introduces generalized Ferrers diagram rank metric codes and establishes a new Singleton bound for them, expanding the theoretical understanding of these codes.
Findings
Established a new Singleton bound for generalized Ferrers diagram rank metric codes
Reproduced existing bounds for specific cases using the new technique
Extended the theoretical framework for non-linear Ferrers diagram rank metric codes
Abstract
In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding