Solving Some Affine Equations over Finite Fields
| Autor: | Dok Nam Lee, Kwang Ho Kim, Sihem Mesnager, Jong Hyok Choe |
|---|---|
| Přispěvatelé: | Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Algebra and Number Theory Mathematics - Number Theory Applied Mathematics Information Theory (cs.IT) Computer Science - Information Theory 010102 general mathematics General Engineering 0102 computer and information sciences 01 natural sciences Prime (order theory) Theoretical Computer Science Combinatorics Finite field 010201 computation theory & mathematics FOS: Mathematics Affine transformation Number Theory (math.NT) [MATH]Mathematics [math] 0101 mathematics Mathematics |
| Zdroj: | Finite Fields and Their Applications Finite Fields and Their Applications, Elsevier, 2020, 68, pp.101746-. ⟨10.1016/j.ffa.2020.101746⟩ |
| ISSN: | 1071-5797 1090-2465 |
| DOI: | 10.1016/j.ffa.2020.101746⟩ |
| Popis: | Let l and k be two integers such that l | k . Define T l k ( X ) : = X + X p l + ⋯ + X p k − 2 l + X p k − l and S l k ( X ) : = X − X p l + ⋯ + ( − 1 ) ( k / l − 1 ) X p k − l , where p is any prime. This paper gives explicit representations of all solutions in F p n to the affine equations T l k ( X ) = a and S l k ( X ) = a , a ∈ F p n . The case p = 2 was solved very recently in [10] . The results of this paper reveal another solution. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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