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Designs, Codes and Cryptography

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11.12.2019

Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes

verfasst von: Cunsheng Ding, Chunming Tang, Vladimir D. Tonchev

Erschienen in: Designs, Codes and Cryptography | Ausgabe 4/2020

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In this paper, the 3-rank of the incidence matrices of 2-designs supported by the minimum weight codewords in a family of ternary linear codes considered in Ding and Li (Discret Math 340(10):2415–2431, 2017) are computed. A lower bound on the minimum distance of the ternary codes spanned by the incidence matrices of these designs is derived, and it is proved that the codes are subcodes of the 4th order generalized Reed–Muller codes.

Nächster Artikel Cryptanalysis of a rank-based signature with short public keys

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Titel: Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes
verfasst von: Cunsheng Ding
Chunming Tang
Vladimir D. Tonchev
Publikationsdatum: 11.12.2019
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 4/2020
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00701-1

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Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes

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