Maximum scattered \(\mathbb{F}_q\)-linear sets of \(\mathrm{PG}(1,q^4)\)

DOI10.1016/j.disc.2017.07.001zbMath1387.51008arXiv1705.00731OpenAlexW2740619074MaRDI QIDQ2411596

Bence Csajbók, Corrado Zanella

Publication date: 24 October 2017

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.00731

zbMATH Keywords

finite projective spacesubgeometryfinite projective linemaximum scattered linear sets

Mathematics Subject Classification ID

Finite affine and projective planes (geometric aspects) (51E15) Combinatorial aspects of finite geometries (05B25)

Related Items (12)

\(r\)-fat linearized polynomials over finite fields ⋮ Linear sets on the projective line with complementary weights ⋮ On the number of roots of some linearized polynomials ⋮ Nuclei and automorphism groups of generalized twisted Gabidulin codes ⋮ On a conjecture about maximum scattered subspaces of \(\mathbb{F}_{q^6}\times\mathbb{F}_{q^6}\) ⋮ A new family of MRD-codes ⋮ A condition for scattered linearized polynomials involving Dickson matrices ⋮ New maximum scattered linear sets of the projective line ⋮ Vertex properties of maximum scattered linear sets of \(\mathrm{PG} ( 1 , q^n )\) ⋮ A Carlitz type result for linearized polynomials ⋮ A class of linear sets in \(\mathrm{PG} (1,q^5)\) ⋮ The geometry of one-weight codes in the sum-rank metric

Uses Software

• GAP
• FinInG

Cites Work

• On the equivalence of linear sets
• Desarguesian spreads and field reduction for elements of the semilinear group
• A new family of linear maximum rank distance codes
• On scattered linear sets of pseudoregulus type in \(\operatorname{PG}(1,q^{t})\)
• Linear sets in finite projective spaces
• A linear set view on KM-arcs
• On the number of slopes of the graph of a function defined on a finite field
• The number of directions determined by a function over a finite field.
• Maximum scattered linear sets and MRD-codes
• On bisecants of Rédei type blocking sets and applications
• Caps on elliptic quadrics
• On embeddings of minimum dimension of \(\mathrm{PG}(n,q)\times \mathrm{PG}(n,q)\)
• Subgeometries and linear sets on a projective line
• \(\mathbb F _q\)-linear blocking sets in \(PG(2,q^4)\)
• Translation ovoids of orthogonal polar spaces
• Blocking sets and derivable partial spreads

This page was built for publication: Maximum scattered \(\mathbb{F}_q\)-linear sets of \(\mathrm{PG}(1,q^4)\)