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arxiv: 1604.05777 · v1 · pith:E3HOJ3Z4new · submitted 2016-04-20 · 🧮 math.AG · cs.IT· math.AC· math.CO· math.IT· math.NT

On Parameters of Subfield Subcodes of Extended Norm-Trace Codes

Heeralal Janwa , Fernando L. Pi\~nero This is my paper
classification 🧮 math.AG cs.ITmath.ACmath.COmath.ITmath.NT
keywords subcodessubfieldcodesdimensionextendedfindnorm--traceparameters
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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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  1. On secret sharing from extended norm-trace curves

    cs.CR 2026-03 unverdicted novelty 4.0

    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.