On interleaved rank metric codes

Vladimir Sidorenko; Wenhui Li; Gerhard Kramer

doi:10.1109/ACCT51235.2020.9383406

On interleaved rank metric codes

Vladimir Sidorenko, Wenhui Li, Gerhard Kramer

Chair of Communications Engineering

Skolkovo Institute of Science and Technology

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

4 Scopus citations

Abstract

Horizontal and vertical interleavings of arbitrary matrix or vector rank metric codes are considered. A necessary and sufficient condition for an interleaved code to be maximum rank distance (MRO) code is obtained. In particular, horizontal interleaving of Gabidulin vector codes over the field {\mathbb{F}_{{qm}}} gives an example of a non-Gabidulin MRD code of length more than m. It is shown that interleaving of Gabidulin codes with different sets of locators can be decoded directly by syndrome decoders. Any other decoder can also be used in the case of different locators after making proposed modification of the received word.

Original language	English
Title of host publication	Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	128-134
Number of pages	7
ISBN (Electronic)	9781665402873
DOIs	https://doi.org/10.1109/ACCT51235.2020.9383406
State	Published - 11 Oct 2020
Event	17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020 - Vitual, Albena, Bulgaria Duration: 11 Oct 2020 → 17 Oct 2020

Publication series

Name	Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020

Conference

Conference	17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020
Country/Territory	Bulgaria
City	Vitual, Albena
Period	11/10/20 → 17/10/20

Access to Document

10.1109/ACCT51235.2020.9383406

Cite this

Sidorenko, V., Li, W., & Kramer, G. (2020). On interleaved rank metric codes. In Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020 (pp. 128-134). Article 9383406 (Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACCT51235.2020.9383406

Sidorenko, Vladimir ; Li, Wenhui ; Kramer, Gerhard. / On interleaved rank metric codes. Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020. Institute of Electrical and Electronics Engineers Inc., 2020. pp. 128-134 (Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020).

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abstract = "Horizontal and vertical interleavings of arbitrary matrix or vector rank metric codes are considered. A necessary and sufficient condition for an interleaved code to be maximum rank distance (MRO) code is obtained. In particular, horizontal interleaving of Gabidulin vector codes over the field {\mathbb{F}_{{qm}}} gives an example of a non-Gabidulin MRD code of length more than m. It is shown that interleaving of Gabidulin codes with different sets of locators can be decoded directly by syndrome decoders. Any other decoder can also be used in the case of different locators after making proposed modification of the received word.",

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Sidorenko, V, Li, W & Kramer, G 2020, On interleaved rank metric codes. in Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020., 9383406, Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020, Institute of Electrical and Electronics Engineers Inc., pp. 128-134, 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020, Vitual, Albena, Bulgaria, 11/10/20. https://doi.org/10.1109/ACCT51235.2020.9383406

On interleaved rank metric codes. / Sidorenko, Vladimir; Li, Wenhui; Kramer, Gerhard.
Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 128-134 9383406 (Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020).

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

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N2 - Horizontal and vertical interleavings of arbitrary matrix or vector rank metric codes are considered. A necessary and sufficient condition for an interleaved code to be maximum rank distance (MRO) code is obtained. In particular, horizontal interleaving of Gabidulin vector codes over the field {\mathbb{F}_{{qm}}} gives an example of a non-Gabidulin MRD code of length more than m. It is shown that interleaving of Gabidulin codes with different sets of locators can be decoded directly by syndrome decoders. Any other decoder can also be used in the case of different locators after making proposed modification of the received word.

AB - Horizontal and vertical interleavings of arbitrary matrix or vector rank metric codes are considered. A necessary and sufficient condition for an interleaved code to be maximum rank distance (MRO) code is obtained. In particular, horizontal interleaving of Gabidulin vector codes over the field {\mathbb{F}_{{qm}}} gives an example of a non-Gabidulin MRD code of length more than m. It is shown that interleaving of Gabidulin codes with different sets of locators can be decoded directly by syndrome decoders. Any other decoder can also be used in the case of different locators after making proposed modification of the received word.

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Sidorenko V, Li W, Kramer G. On interleaved rank metric codes. In Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 128-134. 9383406. (Proceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020). doi: 10.1109/ACCT51235.2020.9383406

On interleaved rank metric codes

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