Csajbók, Bence and Marino, Giuseppe and Polverino, Olga
(2018)
*Classes and equivalence of linear sets in PG(1,q^n).*
JOURNAL OF COMBINATORIAL THEORY SERIES A (157).
pp. 402-426.
ISSN 0097-3165

Text
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## Abstract

The equivalence problem of GF(q)-linear sets of rank n of PG(1,q^n) is investigated, also in terms of the associated variety, projecting configurations,GF(q)-linear blocking sets of Rédei type and MRD-codes. We call an GF(q)-linear set L_U of rank n in PG(W,Fq^n) = PG(1,q^n) simple if for any n-dimensional GF(q)-subspace V of W, L_V is PGammaL(2, q^n)-equivalent to L_U only when U and V lie on the same orbit of GammaL(2,q^n). We prove that U = {(x,Tr(x)) : x \in GF(q^n)} defines a simple GF(q)-linear set for each n. We provide examples of non-simple linear sets not of pseudoregulus type for n > 4 and we prove that all GF(q)-linear sets of rank 4 are simple in PG(1,q^4).

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 06:17 |

Last Modified: | 13 Sep 2018 06:17 |

URI: | http://real.mtak.hu/id/eprint/83771 |

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