Characterizations of a Class of Planar Functions over Finite Fields
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909111193436160 |
|---|---|
| author | Chen, Ruikai Mesnager, Sihem |
| author_facet | Chen, Ruikai Mesnager, Sihem |
| contents | Planar functions, introduced by Dembowski and Ostrom, have attracted much attention in the last decade. As shown in this paper, we present a new class of planar functions of the form $\operatorname{Tr}(ax^{q+1})+\ell(x^2)$ on an extension of the finite field $\mathbb F_{q^n}/\mathbb F_q$. Specifically, we investigate those functions on $\mathbb F_{q^2}/\mathbb F_q$ and construct several typical kinds of planar functions. We also completely characterize them on $\mathbb F_{q^3}/\mathbb F_q$. When the degree of extension is higher, it will be proved that such planar functions do not exist given certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09265 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizations of a Class of Planar Functions over Finite Fields Chen, Ruikai Mesnager, Sihem Number Theory Information Theory 11T06, 12E10, 51E15 Planar functions, introduced by Dembowski and Ostrom, have attracted much attention in the last decade. As shown in this paper, we present a new class of planar functions of the form $\operatorname{Tr}(ax^{q+1})+\ell(x^2)$ on an extension of the finite field $\mathbb F_{q^n}/\mathbb F_q$. Specifically, we investigate those functions on $\mathbb F_{q^2}/\mathbb F_q$ and construct several typical kinds of planar functions. We also completely characterize them on $\mathbb F_{q^3}/\mathbb F_q$. When the degree of extension is higher, it will be proved that such planar functions do not exist given certain conditions. |
| title | Characterizations of a Class of Planar Functions over Finite Fields |
| topic | Number Theory Information Theory 11T06, 12E10, 51E15 |
| url | https://arxiv.org/abs/2303.09265 |