Fernando Hernando

Manuscripts Under Review for Publication:

• Quantum (r,δ)-Locally Recoverable BCH and Homothetic-BCH Codes.
• New Quantum Stabilizer Codes from generalized Monomial-Cartesian Codes constructed using two different generalized Reed-Solomon codes.
• Locally recoverable codes from the matrix-product construction.
• Implementing Basic Arithmetic in 𝔽p via 𝔽2, and Its Application for Computing the Hamming Distance of Linear Codes.
• Impure codes exceeding the pure bounds for quantum local recovery.

Publications in Journals:

1. S. Bodur, F. Hernando, E. Martínez-Moro, D. Ruano: The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval. Comp. Appl. Math. 45, 293 (2026).
2. F. Hernando, G. Quintana-Ortí, M. Grassl: Fast Algorithms for Computing the Minimum Distance of Quantum Codes. ACM Transactions on Quantum Computing, Volume 7, Issue 2, No. 12, 2026.
3. C. Galindo, F. Hernando, H. Martín, R. Matsumoto: Quantum (r,δ)-locally recoverable codes. Finite Fields and Their Applications, Volume 111, 2026.
4. C. Galindo, F. Hernando, H. Martín: New quantum codes from homothetic-BCH codes. Computational and Applied Mathematics, Volume 45, article number 132, (2026).
5. O. Campion, F. Hernando, G. McGuire: New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes. Cryptogr. Commun. (2025).
6. 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)
7. 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).
8. C. Galindo, F. Hernando, R. Matsumoto: Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes. Comp. Appl. Math. 42, 275 (2023).
9. 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) .
10. 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).
11. 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)
12. 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).
13. 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).
14. C. Galindo, F. Hernando, C. Munuera: Locally recoverable J-affine variety codes.Finite Fields and Their Applications 64 (2020).
15. 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).
16. C. Galindo, F. Hernando, R. Matsumoto, D. Ruano: Entanglement-assisted quantum error-correcting codes over arbitrary finite fields. Quantum Information Processing 18:116 (2019).
17. 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.
18. 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).
19. 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).
20. C. Galindo, F. Hernando, R. Matsumoto: Quasi-Cyclic Constructions of Quantum Codes. Finite Fields and Their Applications. Volume 52, July 2018, Pages 261-280.
21. 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).
22. 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).
23. 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.
24. 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
25. 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.
26. 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.
27. 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.
28. 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
29. F. Hernando and D. Ruano: Decoding of Matrix-Product Codes. Journal of Algebra and Its Applications (JAA). Volume No.12, Issue No. 4 (2013).
30. 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
31. 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.
32. 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
33. 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 .
34. 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]
35. 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).
36. 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).
37. 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).