Fernando Hernando

Current Position

Associate Professor (Contratado Doctor Interino).

Professional Address:

Department of Mathematics
Room 2301, third floor.
Universidad Jaume I
Campus Riu Sec, 12071, Castellon de la plana,

Tel. +34 964 728404
Email: carrillf(at)mat.uji.es


Prácticas: Grafos Mathematica

Presentación: Taller de Grafs


(2018-2019) Matemáticas I en informática. Álgebra para ingenieros. Máster de teoría de la información .


Research Interest: Singularities, Algebraic Geometry, Commutative Algebra, Coding Theory, Combinatory and Computation.

Publications in Journals:

  • F. Hernando, F. Igual, G. Quintana-Orti: Fast Algorithms for the Computation of the Minimum Distance of a Random Linear Code. Accepted for publication in ACM Transactions on Mathematical Software (TOMS).
  • C. Galindo, F. Hernando, D. Ruano: Classical and Quantum Evaluation Codes at the Trace Roots. IEEE Transactions on Information Theory. Volume 65, Issue 4, pages 2593-2602 (2019).
  • C. Galindo, F. Hernando, D. Ruano: New binary and ternary LCD codes. IEEE Transactions on Information Theory. Volume 65, Issue 2, pages 1008-1016 (2019).
  • C. Galindo, F. Hernando, R. Matsumoto: Quasi-Cyclic Constructions of Quantum Codes. Finite Fields and Their Applications. Volume 52, July 2018, Pages 261-280.
  • C.Galindo, O. Geil, F. Hernando, D. Ruano: Improved constructions of nested code pairs. IEEE Transactions on Information Theory. Volume 64, Issue 4, pages 2444-2459 (2018).
  • C.Galindo, O. Geil, F. Hernando, D. Ruano: On the distance of stabilizer quantum codes given by J-affine variety codes . Quantum Information Processing, Volumen 16, Issue 4, 16:111 (2017).
  • C. Galindo, F. Hernando, F. Monserrat: The log-canonical threshold of a plane curve. Cambridge Philosophical Society, Volume 160, Issue 3, May 2016, pp. 513-535.
  • C. Galindo, F. Hernando, D. Ruano: Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement . Quantum Information Processing. September 2015, Volume 14, Issue 9, pp 3211-3231
  • C. Galindo, F. Hernando, D. Ruano: New Quantum Codes from Evaluation and Matrix-Product Codes. Finite Fields and Their Applications. 2015, Volume 36, pp 98-120.
  • C. Galindo, F. Hernando: Quantum codes from affine variety codes and their subfield-subcodes . Designs, Codes and Cryptography.July 2015, Volume 76, Issue 1, pp 89-100.
  • F. Hernando, G. McGuire, F. Monserrat: On the Classification of Exceptional Planar Functions over $\mathbb{F}_{p}$. Geometriae Dedicata: Volume 173, Issue 1 (2014), Page 1-35.
  • F.Hernando, M. O'Sullivan and D. Ruano: List decoding repeated codes. Applicable Algebra in Engineering, Communication and Computing,August 2013, Volume 24, Issue 3-4, pp 237-253
  • F. Hernando and D. Ruano: Decoding of Matrix-Product Codes. Journal of Algebra and Its Applications (JAA). Volume No.12, Issue No. 4 (2013).
  • F. Hernando, K. Marshall and M. O'Sullivan: The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes. Design Codes and Cryptography, October 2013, Volume 69, Issue 1, pp 131-142
  • F. Hernando, T. Høholdt, D. Ruano, List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes. Adv. Math. Commun, pp 259 - 272, Volume 6, Issue 3, August 2012.
  • F.Hernando and Gary McGuire: Proof of a Conjecture of Segre and Bartocci on Monomial Hyperovals in Projective Planes. Design Codes and Cryptography, December 2012, Volume 65, Issue 3, pp 275-289
  • F.Hernando and Gary McGuire: Proof of a Conjecture on the Sequence of Exceptional Numbers, Classifying Cyclic Codes and APN Functions . Journal of Algebra, Volume 343, Issue 1, October 2011, Pages 78-92 .
  • F. Hernando, D. Ruano: New linear codes from matrix-product codes with polynomial units. Adv. Math. Commun. 4 (2010), no. 3, 363-367. [File with new quasi-cyclic codes]
  • A. Campillo, F. Delgado, S.M.Gusein-Zade and F. Hernando: Poincaré series of collections of plane valuations. International Journal of Mathematics. Vol. 21, No. 11 (2010).
  • F. Hernando, K. Lally, D. Ruano: Construction and decoding of matrix-product codes from nested codes. Applicable Algebra in Engineering,Communication and Computing, Volume 20, Issue 5, pages 497-507 (2009).
  • Pedro Daniel González Pérez and Fernando Hernando: Quasi-ordinary singularities, essential divisors and Poincaré series . Journal of the London Mathematical Society, 79, No. 3, 780-802 (2009).
  • Peer reviewed conference paper:

  • C. Galindo, F. Hernando, F. Monserrat, R. Pellikann: The Poincaré polynomial of a linear code. Accepted for publication in Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Springer.
  • F.Hernando and Gary McGuire: On the classification of PN and APN Monomial Functions. Finite Fields and Their Applications: Character Sums and Polynomials (Radon Series on Computational and Applied Mathematics), P. Charpin, A. Pott, A. Winterhof (eds.), de Gruyter 2013, 145-164.
  • F.Hernando , M.E. O'Sullivan , E. Popovici and S. Srivastava: Subfield-Subcodes of Generalized Toric codes. 2010 IEEE International Symposium on Information Theory (ISIT 2010), 1125 - 1129.
  • F.Delgado and F. Hernando: On the contact with the polar. Computational commutative and non-commutative algebraic geometry, 74--78, NATO Sci. Ser. III Comput. Syst. Sci., 196, IOS, Amsterdam, 2005.
  • Other Publications:

  • F. Hernando and T. Keilen: alexpoly.lib. A SINGULAR 2.0 library for computing the resolution graph, the semigroup and the Alexander polynomial of plane curve singularities (2003).
  • F. Hernando and D. Ruano: Sixteen New Linear Codes With Plotkin Sum.
  • Preprints:

    PhD Thesis:
    Under the supervison of Prof Felix Delgado de la Mata: Singularities of Quasi-Ordinary Hypersurfaces. University of Valladolid, July 2007.

    Master Dissertation:
    Under the supervison of Prof Felix Delgado de la Mata and Gert Martin Greuel: Computation of the Alexander polynomial of a plane curve singularity and an implementation in Singular. University of Kaiserslautern (2002).