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Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2026 / Cilt: 4 Sayı: 1

Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower

Olav Geil
Stefano Martin
Umberto Martínez-peñas
Diego Ruano
Pages
37–47
Publication Date
2017-01-11
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For general codimension, we give an improved estimate for the highest RGHW.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields.
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Key Findings & Data:In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small.
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Conclusion & Impact:For general codimension, we give an improved estimate for the highest RGHW.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Algebraic geometric codes · Asymptotically good ramp secret sharing schemes · Generalized Hamming weights

Abstract

Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW.

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Cite This Article

Geil, O., Martin, S., Martínez-peñas, U., Ruano, D. (2017). Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 4 Sayı: 1, 37–47. https://doi.org/10.13069/jacodesmath.34390

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References (13)

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