New maximum scattered linear sets of the projective line
| Autor: | Giuseppe Marino, Bence Csajbók, Ferdinando Zullo |
|---|---|
| Přispěvatelé: | Csajbok, B., Marino, G., Zullo, F. |
| Rok vydání: | 2018 |
| Předmět: |
Scattered subspace
Algebra and Number Theory Applied Mathematics 010102 general mathematics Minimum distance General Engineering 0102 computer and information sciences Linear set MRD-code Scattered subspace Trinomial 51E20 51E22 05B25 01 natural sciences Linear subspace Theoretical Computer Science Combinatorics 010201 computation theory & mathematics Projective line FOS: Mathematics Mathematics - Combinatorics MRD-code Combinatorics (math.CO) 0101 mathematics Equivalence (formal languages) Linear set Mathematics |
| Zdroj: | Finite Fields and Their Applications. 54:133-150 |
| ISSN: | 1071-5797 |
| DOI: | 10.1016/j.ffa.2018.08.001 |
| Popis: | In [2] and [18] are presented the first two families of maximum scattered F q -linear sets of the projective line PG ( 1 , q n ) . More recently in [22] and in [5] , new examples of maximum scattered F q -subspaces of V ( 2 , q n ) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the F q -linear sets presented in [22] and in [5] , for n = 6 , 8 , are new. Also, for q odd, q ≡ ± 1 , 0 ( mod 5 ) , we present new examples of maximum scattered F q -linear sets in PG ( 1 , q 6 ) , arising from trinomial polynomials, which define new F q -linear MRD-codes of F q 6 × 6 with dimension 12, minimum distance 5 and left idealiser isomorphic to F q 6 . |
| Databáze: | OpenAIRE |
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