414 KB39 KB200820252020Bartoli, DanieleZanella, CorradoZullo, Ferdinandoštevilka:1letnik:19str. 125-145ISSN:1855-3974COBISSID_HOST:43524099URN:URN:NBN:SI:doc-OYOXST37enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanealinearized polynomiallinearizirani polinomMRD-codeMRD-kodarazpršena linearna množicascattered linear setA new family of maximum scattered linear sets in PG(1, qsup6)|We generalize the example of linear set presented by the last two authors in "Vertex properties of maximum scattered linear sets of ?$\mathrm{PG}(1,q^n)$?" (2019) to a more general family, proving that such linear sets are maximum scattered when ?$q$? is odd and, apart from a special case, they are are new. This solves an open problem posed in "Vertex properties of maximum scattered linear sets of ?$\mathrm{PG}(1,q^n)$?" (2019). As a consequence of Sheekey's results in "A new family of linear maximum rank distance codes" (2016), this family yields to new MRD-codes with parameters ?$(6,6,q;5)$?Posplošimo primer linearne množice iz članka zadnjih dveh avtorjev "Vertex properties of maximum scattered linear sets of ?$\mathrm{PG}(1,q^n)$?" (2019) na splošnejšo družino, pri čemer dokažemo, da so takšne linearne množice maksimalno razpršene, kadar je ?$q$? lih, in da so, razen v enem posebnem primeru, nove. S tem rešimo odprt problem iz članka "Vertex properties of maximum scattered linear sets of ?$\mathrm{PG}(1,q^n)$?" (2019). Upoštevaje Sheekeyeve rezultate iz članka "A new family of linear maximum rank distance codes" (2016), ta družina vodi k novim MRD-kodam s parametri ?$(6,6,q;5)$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije