IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Information Theory and Its Applications
On Asymptotically Good Ramp Secret Sharing Schemes
Olav GEILStefano MARTINUmberto MARTÍNEZ-PEÑASRyutaroh MATSUMOTODiego RUANO
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2017 Volume E100.A Issue 12 Pages 2699-2708

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Abstract

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.

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© 2017 The Institute of Electronics, Information and Communication Engineers
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