Codes Endowed With the Rank Metric
Elisa Gorla, Alberto Ravagnani
TL;DR
This paper reviews the main theoretical results on rank-metric codes, focusing on their combinatorial properties, duality, and the structure of optimal codes and anticodes in the rank metric.
Contribution
It provides a comprehensive comparison of rank-metric codes in vector and matrix forms and explores the combinatorial structure of MRD codes and anticodes.
Findings
Comparison of rank-metric codes in different representations
Analysis of duality and MacWilliams identities for rank-metric codes
Structural insights into MRD codes and optimal anticodes
Abstract
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix representation. We then investigate the combinatorial structure of MRD codes and optimal anticodes in the rank metric, describing how they relate to each other.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Cooperative Communication and Network Coding