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Cryptography and Communications

Erschienen in:

01.12.2017

Five classes of optimal two-weight linear codes

verfasst von: Gaojun Luo, Xiwang Cao

Erschienen in: Cryptography and Communications | Ausgabe 6/2018

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Abstract

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, data storage systems, strongly regular graphs and some other fields. Two-weight linear codes are particularly interesting since they are closely related to finite geometry, combinatorial designs, graph theory. In this paper, we propose five classes of two-Lee-weight codes over the ring \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). By the Gray map, we obtain five classes of linear codes with two weights over \(\mathbb {F}_{q}\) and these linear codes are optimal with respect to the Griesmer bound. As applications, we can employ these linear codes to construct secret sharing schemes with nice access structures.

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Titel: Five classes of optimal two-weight linear codes
verfasst von: Gaojun Luo
Xiwang Cao
Publikationsdatum: 01.12.2017
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 6/2018
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-017-0272-3

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