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A geometric approach to rank metric codes and a classification of constant weight codes

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Abstract

In this work we develop a geometric approach to the study of rank metric codes. Using this method, we introduce a simpler definition for generalized rank weight of linear codes. We give a complete classification of constant rank weight code and we give their generalized rank weights.

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Acknowledgements

I would like to thank Rakhi Pratihar and Prof. Sudhir Ghorparde for their valuable comments and suggestions on this work. I also would like to thank the anonymous reviewer who introduced me to linear sets.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India

    Tovohery Hajatiana Randrianarisoa

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  1. Tovohery Hajatiana Randrianarisoa
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Correspondence to Tovohery Hajatiana Randrianarisoa.

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Communicated by I. Landjev.

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The author is supported by the Swiss National Science Foundation Grant No. 181446.

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Randrianarisoa, T.H. A geometric approach to rank metric codes and a classification of constant weight codes. Des. Codes Cryptogr. 88, 1331–1348 (2020). https://doi.org/10.1007/s10623-020-00750-x

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  • DOI: https://doi.org/10.1007/s10623-020-00750-x

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