A lower bound for constant dimension codes from multi-component lifted MRD codes
Anna-Lena Trautmann
TL;DR
This paper derives a lower bound for the size of constant dimension codes by analyzing unions of lifted MRD codes, providing a new explicit formula for their cardinality.
Contribution
It introduces an explicit formula for the cardinality of unions of lifted MRD codes, leading to a new lower bound for constant dimension codes.
Findings
Derived an explicit formula for the cardinality of unions of lifted MRD codes.
Established a new lower bound for the size of constant dimension codes.
Enhanced understanding of the structure of constant dimension codes.
Abstract
In this work we investigate unions of lifted MRD codes of a fixed dimension and minimum distance and derive an explicit formula for the cardinality of such codes. This will then imply a lower bound on the cardinality of constant dimension codes.
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Error Correcting Code Techniques