Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes

DOI10.1007/s10623-012-9624-3zbMath1266.51013arXiv1010.3965OpenAlexW2003871532WikidataQ62582187 ScholiaQ62582187MaRDI QIDQ690674

Gary McGuire, Fernando Hernando

Publication date: 28 November 2012

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3965

zbMATH Keywords

hyperovalovalabsolutely irreducibleBezoutmonomial hyperoval

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes and caps in Galois spaces (51E22) Blocking sets, ovals, (k)-arcs (51E21) Polynomials over finite fields (11T06)

Related Items (12)

Exceptional scattered polynomials ⋮ Classification of permutation polynomials of the form \(x^3g(x^{q-1})\) of \(\mathbb{F}_{q^2}\) where \(g(x)=x^3+bx+c\) and \(b, c \in\mathbb{F}_q^*\) ⋮ Complete characterization of some permutation polynomials of the form \(x^r (1+ax^{s_1(q-1)}+bx^{s_2(q-1)})\) over \(\mathbb{F}_{q^2}\) ⋮ On a generalization of planar functions ⋮ Almost perfect and planar functions ⋮ On the classification of exceptional scattered polynomials ⋮ On the classification of exceptional planar functions over \(\mathbb F_p\) ⋮ Planar functions over fields of characteristic two ⋮ Hyperovals in Knuth's binary semifield planes ⋮ On the classification of hyperovals ⋮ Low-degree planar polynomials over finite fields of characteristic two ⋮ Planar functions and perfect nonlinear monomials over finite fields

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• Double-error-correcting cyclic codes and absolutely irreducible polynomials over \(\text{GF}(2)\)
• Hyperovals in PG(2,16)
• Permutation Properties of the Polynomials 1 + x + ⋯+ x k Over a Finite Field
• Ovali ed altre curve nei piani di Galois di caratteristica due

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