Article

On Minimal and Quasi-minimal Linear Codes

Authors:

Gérard D. Cohen,

Sihem Mesnager,

Alain PateyAuthors Info & Claims

IMACC 2013: Proceedings of the 14th IMA International Conference on Cryptography and Coding - Volume 8308

Pages 85 - 98

https://doi.org/10.1007/978-3-642-45239-0_6

Published: 17 December 2013 Publication History

Abstract

Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We here study minimal codes, give new bounds and properties and exhibit families of minimal linear codes. We also introduce and study the notion of quasi-minimal linear codes, which is a relaxation of the notion of minimal linear codes, where two non-zero codewords have the same support if and only if they are linearly dependent.

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Cited By

Mesnager S(2018)Linear codes with few weights from weakly regular bent functions based on a generic constructionCryptography and Communications10.1007/s12095-016-0186-59:1(71-84)Online publication date: 17-Dec-2018
https://dl.acm.org/doi/10.1007/s12095-016-0186-5
Chang SHyun J(2018)Linear codes from simplicial complexesDesigns, Codes and Cryptography10.1007/s10623-017-0442-586:10(2167-2181)Online publication date: 1-Oct-2018
https://dl.acm.org/doi/10.1007/s10623-017-0442-5
Liu ZWu X(2016)The fullrank value functionDesigns, Codes and Cryptography10.1007/s10623-015-0159-281:2(297-315)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s10623-015-0159-2
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cover image Guide Proceedings

IMACC 2013: Proceedings of the 14th IMA International Conference on Cryptography and Coding - Volume 8308

December 2013

363 pages

ISBN:9783642452383

Editor:
Martijn Stam
Dept. of Computer Science, University of Bristol, Bristol, UK

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 December 2013

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Cited By

Mesnager S(2018)Linear codes with few weights from weakly regular bent functions based on a generic constructionCryptography and Communications10.1007/s12095-016-0186-59:1(71-84)Online publication date: 17-Dec-2018
https://dl.acm.org/doi/10.1007/s12095-016-0186-5
Chang SHyun J(2018)Linear codes from simplicial complexesDesigns, Codes and Cryptography10.1007/s10623-017-0442-586:10(2167-2181)Online publication date: 1-Oct-2018
https://dl.acm.org/doi/10.1007/s10623-017-0442-5
Liu ZWu X(2016)The fullrank value functionDesigns, Codes and Cryptography10.1007/s10623-015-0159-281:2(297-315)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s10623-015-0159-2
Liu JMesnager SChen L(2015)Secret Sharing Schemes with General Access StructuresRevised Selected Papers of the 11th International Conference on Information Security and Cryptology - Volume 958910.1007/978-3-319-38898-4_20(341-360)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-38898-4_20
Chabanne HCohen GPatey A(2013)Towards Secure Two-Party Computation from the Wire-Tap ChannelInformation Security and Cryptology -- ICISC 201310.1007/978-3-319-12160-4_3(34-46)Online publication date: 27-Nov-2013
https://dl.acm.org/doi/10.1007/978-3-319-12160-4_3

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