Teaching
Matemáticas I en informática. Álgebra para ingenieros. Máster de teoría de la información .
Research
Research Interest: Singularities, Algebraic Geometry,
Commutative Algebra, Coding Theory, Combinatory and Computation.
Publications in Journals:
- Beatriz Barbero-Lucas and Fernando Hernando and Helena Mart'in-Cruz and Gary McGuire MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes.
Quantum Information Processing, Volume 23, article number 86, (2024).
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- C. Galindo, F. Hernando, R. Matsumoto Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes. Comp. Appl. Math. 42, 275 (2023).
- C. Galindo, F. Hernando, H. Martín-Cruz, D. Ruano: Stabilizer quantum codes defined by trace-depending polynomials. Finite Fields and their Applications. Volume 87, 102138 (2023) .
- G.Quintana-Ortí, F. Hernando, F. D. Igual Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Multicomputers. ACM Transactions on Mathematical Software,Volume 49, 2023, pp 1–24.
- C. Galindo, F. Hernando. On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes . Designs, Codes and Cryptography volume 90, pages1103–1112 (2022)
- C. Galindo, F. Hernando, D. Ruano. Entanglement-assisted quantum error correcting codes from RS codes and BCH codes with extension degree 2. Quantum Information Processing volume 20, Article number: 158 (2021).
- F. Hernando, G. McGuire, F. Monserrat, J.J. Moyano-Fernández Quantum codes from a new construction of self-orthogonal algebraic geometry codes. Quantum Information Processing volume 19, Article number: 117 (2020).
- C. Galindo, F. Hernando, C. Munuera Locally recoverable J-affine variety codes.Finite Fields and Their Applications 64 (2020).
- C. Galindo, F. Hernando, R. Matsumoto, D. Ruano Asymmetric entanglement-assisted quantum error-correcting codes and BCH codes. IEEE Access. Volume 8, pages 18571-18579 (2020).
- C. Galindo, F. Hernando, R. Matsumoto, D. Ruano: Entanglement-assisted quantum error-correcting codes over arbitrary finite fields. Quantum Information Processing 18:116 (2019).
- F. Hernando, F. Igual, G. Quintana-Orti: Fast Algorithms for the Computation of the Minimum Distance of a Random
Linear Code. ACM Transactions on
Mathematical Software (TOMS). Volume 45 Issue 2, June 2019.
- 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.
Designs 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.
Designs 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. Peer reviewed conference paper:Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. 19 September 2018.
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:
C. Galindo, F. Hernando, H. Martín Optimal (r,δ)-LRCs from zero-dimensional affine variety codes and their subfield-subcode.
C. Galindo, F. Hernando, C. Munuera, D. Ruano Locally recoverable codes from the matrix-product construction .
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).