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Wei-type duality theorems for rank metric codes

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Abstract

We extend and provide new proofs of the Wei-type duality theorems, due to Ducoat and Ravagnani, for Gabidulin–Roth rank-metric codes and for Delsarte rank-metric codes. These results follow as corollaries from fundamental Wei-type duality theorems that we prove for certain general combinatorial structures.

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Acknowledgements

We gratefully thank the referees for their excellent comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, UNSW Sydney, 2052, Sydney, NSW, Australia

    Thomas Britz

  2. School of Mathematical Sciences, Monash University, 3800, Clayton, VIC, Australia

    Adam Mammoliti

  3. Department of Mathematics and Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto, 860-8555, Japan

    Keisuke Shiromoto

Authors
  1. Thomas Britz
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  2. Adam Mammoliti
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  3. Keisuke Shiromoto
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Correspondence to Thomas Britz.

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Keisuke Shiromoto was supported by JSPS KAKENHI Grant Number 16KK0103.

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Codes, Cryptology and Curves”.

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Britz, T., Mammoliti, A. & Shiromoto, K. Wei-type duality theorems for rank metric codes. Des. Codes Cryptogr. 88, 1503–1519 (2020). https://doi.org/10.1007/s10623-019-00688-9

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  • DOI: https://doi.org/10.1007/s10623-019-00688-9

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