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Constructions of optimal Ferrers diagram rank metric codes

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Abstract

Subspace codes and constant dimension codes have become a widely investigated research topic due to their significance to error control in random linear network coding. Rank metric codes in Ferrers diagrams can be used to construct good subspace codes and constant dimension codes. In this paper, three constructions of Ferrers diagram rank metric codes are presented. The first two constructions are based on subcodes of maximum rank distance codes, and the last one generates new codes from known Ferrers diagram rank metric codes. Each of these constructions produces optimal codes with different diagrams and parameters for which no optimal construction was known before.

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Acknowledgements

The authors express their gratitude to the anonymous reviewers for their detailed and constructive comments which are very helpful to the improvement of this paper, and to Prof. Tuvi Etzion, the Associate Editor, for his insightful advice and excellent editorial job.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Tao Zhang & Gennian Ge

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  1. Tao Zhang
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  2. Gennian Ge
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Correspondence to Tao Zhang.

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Communicated by T. Etzion.

Gennian Ge: Research supported by the National Natural Science Foundation of China under Grant Nos. 11431003 and 61571310, Beijing Scholars Program, Beijing Hundreds of Leading Talents Training Project of Science and Technology, and Beijing Municipal Natural Science Foundation.

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Zhang, T., Ge, G. Constructions of optimal Ferrers diagram rank metric codes. Des. Codes Cryptogr. 87, 107–121 (2019). https://doi.org/10.1007/s10623-018-0491-4

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  • DOI: https://doi.org/10.1007/s10623-018-0491-4

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