research-article

Linear codes from perfect nonlinear mappings and their secret sharing schemes

Authors:

C. Carlet,

C. Ding,

J. YuanAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 51, Issue 6

Pages 2089 - 2102

https://doi.org/10.1109/TIT.2005.847722

Published: 01 June 2005 Publication History

Abstract

In this paper, error-correcting codes from perfect nonlinear mappings are constructed, and then employed to construct secret sharing schemes. The error-correcting codes obtained in this paper are very good in general, and many of them are optimal or almost optimal. The secret sharing schemes obtained in this paper have two types of access structures. The first type is democratic in the sense that every participant is involved in the same number of minimal-access sets. In the second type of access structures, there are a few dictators who are in every minimal access set, while each of the remaining participants is in the same number of minimal-access sets.

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Linear codes from perfect nonlinear mappings and their secret sharing schemes

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IEEE Transactions on Information Theory Volume 51, Issue 6

June 2005

328 pages

ISSN:0018-9448

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IEEE Press

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Published: 01 June 2005

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https://dl.acm.org/doi/10.1109/TIT.2024.3408882
Yoon Hyun JJeong JLee Y(2024)Infinite Families of Few Weight Optimal Binary Linear Codes From Multivariable FunctionsIEEE Transactions on Information Theory10.1109/TIT.2024.340679870:10(6912-6931)Online publication date: 1-Oct-2024
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Wu HYang JFeng K(2023)The Weight Distributions of Two Classes of Linear Codes From Perfect Nonlinear FunctionsIEEE Transactions on Information Theory10.1109/TIT.2023.334822870:6(4102-4109)Online publication date: 29-Dec-2023
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