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Cryptography and Communications

Erschienen in:

04.06.2019

A family of distance-optimal minimal linear codes with flexible parameters

verfasst von: Xia Li, Cuiling Fan, Xiaoni Du

Erschienen in: Cryptography and Communications | Ausgabe 3/2020

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Abstract

Due to their wide applications in communications, data storage and cryptography, linear codes have received much attention in the past decades. The objective of this paper is to construct a family of linear codes over \({\mathbb F}_{q}\), where q is a prime power. This family of codes has length (q^k − 1)t, dimension ek, where k ≥ 2 and e, t are arbitrary integers with 2 ≤ e ≤ t . In some cases, this class of linear codes is distance-optimal with respect to the Griesmer bound. The weight distribution of this family of linear codes is also determined. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.

Vorheriger Artikel Three deterministic constructions of compressed sensing matrices with low coherence

Nächster Artikel A class of exponential sums and sequence families

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Titel: A family of distance-optimal minimal linear codes with flexible parameters
verfasst von: Xia Li
Cuiling Fan
Xiaoni Du
Publikationsdatum: 04.06.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 3/2020
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00373-7

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