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Journals / Ikonion Journal of Mathematics / 2026 / Volume: 8 Issue: 1

On the Carlet's Bivariate APN Construction and Representations of Dobbertin Power Functions

İlksen Acunalp Erleblebici(ORTA DOĞU TEKNİK ÜNİVERSİTESİ)0009-0007-7350-7645
Ahmet Sınak(AKDENİZ ÜNİVERSİTESİ)0000-0002-1071-765X
Oğuz Yayla(ORTA DOĞU TEKNİK ÜNİVERSİTESİ)0000-0001-8945-2780
Pages
—
Publication Date
2026-07-16
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AI Summary & Key Takeaways

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

In the second part, we study the representation of the Dobbertin power function following methods given by Budaghyan et al. in 2022 and give new representations for this kind of functions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we present necessary and sufficient conditions on some families of bivariate and biprojective APN functions.
📊
Key Findings & Data:In the first part, we follow the extended methods given by Calderini et al in 2021, and give sufficient and necessary conditions for Carlet's bivariate APN functions.
💡
Conclusion & Impact:In the second part, we study the representation of the Dobbertin power function following methods given by Budaghyan et al. in 2022 and give new representations for this kind of functions.
🔬Design:Research Article
📍Scope:2021 Verileri
⚙️Variables:APN functions · bivariate APN construction · Dobbertin power function

Abstract

In this paper we present necessary and sufficient conditions on some families of bivariate and biprojective APN functions. In the first part, we follow the extended methods given by Calderini et al in 2021, and give sufficient and necessary conditions for Carlet's bivariate APN functions. We also give APN-ness conditions for biprojective functions in some special cases. In the second part, we study the representation of the Dobbertin power function following methods given by Budaghyan et al. in 2022 and give new representations for this kind of functions.

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Cite This Article

Erleblebici, İ. A., Sınak, A., Yayla, O. (2026). On the Carlet's Bivariate APN Construction and Representations of Dobbertin Power Functions. Ikonion Journal of Mathematics, Volume: 8 Issue: 1. https://doi.org/10.54286/ikjm.1836416

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