Codes Endowed with the Rank Metric

Elisa Gorla; Alberto Ravagnani

doi:10.1007/978-3-319-70293-3_1

Codes Endowed with the Rank Metric

Elisa Gorla, Alberto Ravagnani

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

3 Citations (Scopus)

Abstract

We review the main results of the theory of error-correcting codes with the rank metric, introducing combinatorial techniques for their analysis. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix representation. We then investigate the structure of MRD codes and cardinality-optimal anticodes in the rank metric, describing how they relate to each other.

Original language	English
Title of host publication	Signals and Communication Technology
Publisher	Springer
Pages	3-23
Number of pages	21
DOIs	https://doi.org/10.1007/978-3-319-70293-3_1
Publication status	Published - 2018
Externally published	Yes

Publication series

Name	Signals and Communication Technology
ISSN (Print)	1860-4862
ISSN (Electronic)	1860-4870

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10.1007/978-3-319-70293-3_1

Cite this

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AB - We review the main results of the theory of error-correcting codes with the rank metric, introducing combinatorial techniques for their analysis. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix representation. We then investigate the structure of MRD codes and cardinality-optimal anticodes in the rank metric, describing how they relate to each other.

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Codes Endowed with the Rank Metric

Abstract

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