On the Carlet’s Bivariate APN Construction and Representations of Dobbertin Power Functions
Ikonion Journal of Mathematics, cilt.8, sa.1, ss.26-43, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.54286/ikjm.1836416
- Dergi Adı: Ikonion Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.26-43
- Anahtar Kelimeler: APN functions, Bivariate APN construction, Dobbertin power function
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
In this paper we present necessary and sufficient conditions on some families of bivariate and biprojective almost perfect nonlinear (APN) functions. In the first part, we follow the extended methods given by Calderini et al in 2021, and give necessary and sufficient 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.