• closedAccess   On the classification of exceptional planar functions over Fp 

      Hernando, Fernando; McGuire, Gary; Monserrat, Francisco Springer Netherlands (2014-12)
      We will present many strong partial results towards a classification of exceptional planar/PN monomial functions on finite fields. The techniques we use are the Weil bound, Bézout’s theorem, and Bertini’s theorem.
    • closedAccess   Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes 

      Hernando, Fernando; McGuire, Gary Springer US (2012-02)
      The existence of certain monomial hyperovals D(xk) in the finite Desarguesian projective plane PG(2, q), q even, is related to the existence of points on certain projective plane curves gk(x, y, z). Segre showed that some ...
    • openAccess   Quantum codes from a new construction of self-orthogonal algebraic geometry codes 

      Hernando, Fernando; McGuire, Gary; Monserrat, Francisco; Moyano-Fernández, Julio José Springer (2020)
      We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results ...