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Designs, Codes and Cryptography

Erschienen in:

18.04.2018

Several classes of linear codes with a few weights from defining sets over $\mathbb {F}_p+u\mathbb {F}_p$

verfasst von: Haibo Liu, Qunying Liao

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2019

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Abstract

Recently, linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. Results have shown that some optimal codes can be acquired if the defining sets are well chosen over finite fields. In this paper, we investigate the Lee-weight distribution of linear codes over the ring $\mathbb {F}_p +u\mathbb {F}_p$ (p is an odd prime) based on defining sets by employing exponential sums. We then determine the explicit complete weight enumerator for the images of these linear codes under the Gray map. A class of constant weight codes that meets the Griesmer bound for constructing optimal constant composition codes achieving the LVFC bound is also presented.

Vorheriger Artikel Secure simultaneous bit extraction from Koblitz curves

Nächster Artikel Involutory differentially 4-uniform permutations from known constructions

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Titel: Several classes of linear codes with a few weights from defining sets over
verfasst von: Haibo Liu
Qunying Liao
Publikationsdatum: 18.04.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0478-1

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Several classes of linear codes with a few weights from defining sets over \(\mathbb {F}_p+u\mathbb {F}_p\)

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