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On asymptotically good ramp secret sharing schemes
Olav Geil, Stefano Martin, Umberto Martínez-Peñas, Ryutaroh Mats · 2015-02-19 · via cs.IT updates on arXiv.org

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. 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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