Wei-type duality theorems for rank metric codes

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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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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Keywords

  • Rank-metric code
  • Wei’s Duality Theorem
  • Demimatroid

Mathematics Subject Classification

  • 94B05
  • 05B35
  • 06A07