Csajbók, Bence and Marino, Giuseppe and Zullo, Ferdinando
(2018)
*New maximum scattered linear sets of the projective line.*
Finite Fields and their Applications (54).
pp. 133-150.
ISSN 1071-5797

Text
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## Abstract

In [A. Blokhuis, M. Lavrauw: Scattered spaces with respect to a spread in PG(n,q), Geom. Dedicata 81 (2000), 231--243.] and [G. Lunardon, O. Polverino: Blocking Sets and Derivable Partial Spreads, J. Algebraic Combin. 14 (2001), 49-56.] are presented the first two families of maximum scattered GF(q)-linear sets of the projective line PG(1,q^n). More recently in [J. Sheekey: A new family of linear maximum rank distance codes, Adv. Math. Commun. 10(3) (2016), 475-488.] and in [B. Csajbók, G. Marino, O. Polverino, C. Zanella: A new family of MRD-codes, Linear Algebra Appl. 548 (2018), 203-220.], new examples of maximum scattered GF(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 GF(q)-linear sets presented in [J. Sheekey: A new family of linear maximum rank distance codes, Adv. Math. Commun. 10(3) (2016), 475-488.] and in [B. Csajbók, G. Marino, O. Polverino, C. Zanella: A new family of MRD-codes, Linear Algebra Appl. 548 (2018), 203-220.], for n=6,8, are new. Also, for q odd, q congruent to 1, -1, or 0 (mod 5), we present new examples of maximum scattered GF(q)-linear sets in PG(1,q^6), arising from trinomial polynomials, which define new GF(q)-linear MRD-codes of GF(q)^6×6 with dimension 12, minimum distance 5 and left idealiser isomorphic to GF(q^6).

Item Type: | Article |
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Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria |

Depositing User: | Bence Csajbók |

Date Deposited: | 13 Sep 2018 06:19 |

Last Modified: | 13 Sep 2018 06:19 |

URI: | http://real.mtak.hu/id/eprint/83793 |

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