494 KB49 KB200820252019Csajbók, BenceMarino, GiuseppePolverino, Olgaletnik:16številka:2str. 585-608ISSN:1855-3966COBISSID_HOST:18813529URN:URN:NBN:SI:doc-QS3ME9M1enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneadirectionlinear setlinearized polynomiallinearizirani polinomlinearna množicasmerA Carlitz type result for linearized polynomials|For an arbitrary ?$q$?-polynomial ?$f$? over ?$\mathbb F_{q^n}$? we study the problem of finding those ?$q$?-polynomials ?$g$? over ?$\mathbb F_{q^n}$? for which the image sets of ?$f(x)/x$? and ?$g(x)/x$? coincide. For ?$n \leq 5$? we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of ?$\mathrm{PG}(1, q^5)$?Za vsak ?$q$?-polinom ?$f$? nad ?$\mathbb F_{q^n}$? obravnavamo problem iskanja tistih ?$q$?-polinomov ?$g$? nad ?$\mathbb F_{q^n}$?, za katere množici slik funkcij ?$f(x)/x$? in ?$f(x)/x$? sovpadata. Za ?$n \leq 5$? podamo potrebne in zadostne pogoje in nato uporabimo naš rezultat pri obravnavi maksimalno razpršenih linearnih množic iz ?$\mathrm{PG}(1, q^5)$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije