A linear set view on KM-arcs

DOI10.1007/s10801-015-0661-7zbMath1346.51002arXiv1512.04818OpenAlexW3100332170MaRDI QIDQ737977

Geertrui Van de Voorde, Maarten De Boeck

Publication date: 12 August 2016

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.04818

zbMATH Keywords

\((0,2,t)\)-arcKM-arcset of even typetranslation arc

Mathematics Subject Classification ID

Blocking sets, ovals, (k)-arcs (51E21) Combinatorial structures in finite projective spaces (51E20)

Related Items (23)

\(r\)-fat linearized polynomials over finite fields ⋮ Linear sets on the projective line with complementary weights ⋮ ON THE PRODUCT OF ELEMENTS WITH PRESCRIBED TRACE ⋮ Maximum scattered \(\mathbb{F}_q\)-linear sets of \(\mathrm{PG}(1,q^4)\) ⋮ The weight distributions of linear sets in \(\mathrm{PG}(1,q^5)\) ⋮ On the number of roots of some linearized polynomials ⋮ Classifications and constructions of minimum size linear sets on the projective line ⋮ Cones from maximum \(h\)-scattered linear sets and a stability result for cylinders from hyperovals ⋮ Two pointsets in \(\mathrm{PG}(2,q^n)\) and the associated codes ⋮ On linear sets of minimum size ⋮ Classes and equivalence of linear sets in \(\mathrm{PG}(1,q^{n})\) ⋮ On bisecants of Rédei type blocking sets and applications ⋮ On KM-arcs in small Desarguesian planes ⋮ On the intersection problem for linear sets in the projective line ⋮ On the intersection distribution of degree three polynomials and related topics ⋮ Polar coordinates view on KM-arcs ⋮ Rank-metric codes, linear sets, and their duality ⋮ A Carlitz type result for linearized polynomials ⋮ Generalizing Korchmáros-Mazzocca arcs ⋮ On KM-arcs in non-Desarguesian projective planes ⋮ Translation hyperovals and \(\mathbb{F}_2\)-linear sets of pseudoregulus type ⋮ The geometry of one-weight codes in the sum-rank metric ⋮ The geometric field of linearity of linear sets

Uses Software

• FinInG

Cites Work

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• Codes of Desarguesian projective planes of even order, projective triads and \((q+t,t)\)-arcs of type \((0, 2, t)\)
• Laguerre planes of even order and translation ovals
• On \((q+t,t)\)-arcs of type \((0,2,t)\)
• Subgeometries and linear sets on a projective line
• An upper bound for the minimum weight of the dual codes of desarguesian planes
• Field reduction and linear sets in finite geometry
• On (q + t)-arcs of type (0, 2, t) in a desarguesian plane of order q

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