For an arbitrary $q$-polynomial $f$ over $F_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $F_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $nleq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $PG(1,q^5)$. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.

A Carlitz type result for linearized polynomials

Giuseppe Marino;
2019

Abstract

For an arbitrary $q$-polynomial $f$ over $F_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $F_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $nleq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $PG(1,q^5)$. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM.
File in questo prodotto:
File Dimensione Formato  
1651-8462-1-PB.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Dominio pubblico
Dimensione 449.17 kB
Formato Adobe PDF
449.17 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/753624
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 11
social impact