Fernando Hernando

Manuscripts Under Review for Publication:

• New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes
• Quantum (r,δ)-locally recoverable codes
• Fast Algorithms for Computing the Minimum Distance of Quantum Codes
• Locally recoverable codes from the matrix-product construction

Publications in Journals:

1. C. Galindo, F. Hernando, H. Martín: Optimal (r,δ)-LRCs from zero-dimensional affine variety codes and their subfield-subcode. Designs, Codes and Cryptography, Volume 92, pages 2549–2586, (2024)
2. B. Barbero-Lucas, F. Hernando, H. Martín-Cruz, G. McGuire: MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes. Quantum Information Processing, Volume 23, article number 86, (2024). .
3. C. Galindo, F. Hernando, R. Matsumoto: Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes. Comp. Appl. Math. 42, 275 (2023).
4. 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) .
5. 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, pp 1–24, (2023).
6. 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)
7. 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).
8. 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).
9. C. Galindo, F. Hernando, C. Munuera: Locally recoverable J-affine variety codes.Finite Fields and Their Applications 64 (2020).
10. 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).
11. C. Galindo, F. Hernando, R. Matsumoto, D. Ruano: Entanglement-assisted quantum error-correcting codes over arbitrary finite fields. Quantum Information Processing 18:116 (2019).
12. 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.
13. 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).
14. 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).
15. C. Galindo, F. Hernando, R. Matsumoto: Quasi-Cyclic Constructions of Quantum Codes. Finite Fields and Their Applications. Volume 52, July 2018, Pages 261-280.
16. 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).
17. 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).
18. 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.
19. 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
20. 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.
21. 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.
22. 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.
23. 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
24. F. Hernando and D. Ruano: Decoding of Matrix-Product Codes. Journal of Algebra and Its Applications (JAA). Volume No.12, Issue No. 4 (2013).
25. 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
26. 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.
27. 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
28. 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 .
29. 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]
30. 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).
31. 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).
32. P.D. González Pérez, F. Hernando: Quasi-ordinary singularities, essential divisors and Poincaré series . Journal of the London Mathematical Society, 79, No. 3, 780-802 (2009).

Peer reviewed conference papers:

• 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.

PhD Thesis:
Under the supervision of Prof Felix Delgado de la Mata: Singularities of Quasi-Ordinary Hypersurfaces.

Master's Dissertation:
Under the supervision 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).