Ramp secret sharing schemes from extended norm-trace curves achieve strong parameters and a second security layer, with the footprint approach shown to be an application of the enhanced Goppa bound.
On Parameters of Subfield Subcodes of Extended Norm-Trace Codes
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In this article we describe how to find the parameters of subfield subcodes of extended Norm--Trace codes. With a Gr\"obner basis of the ideal of the $\mathbb{F}_{q^r}$ rational points of the Norm--Trace curve one can determine the dimension of the subfield subcodes or the dimension of the trace code. We also find a BCH--like bound from the minimum distance of the original supercode.
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On secret sharing from extended norm-trace curves
Ramp secret sharing schemes from extended norm-trace curves achieve strong parameters and a second security layer, with the footprint approach shown to be an application of the enhanced Goppa bound.