Rodrigo San-José

I am currently a Presidential Postdoctoral Fellow at Virginia Tech. I used to be a postdoctoral researcher with IMUVa, University of Valladolid. My main research interest is algebraic coding theory, particularly its connections with commutative algebra and algebraic geometry, and its applications to quantum error correction and cryptography.
Here are some quotes that I like:

• Related to work: [1], [2] (other version [3]), [4], [5].
• Literature: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11].
• Miscellaneous: [1], [2], [3], [4].

My full name is Rodrigo San José Rubio.

10. R. San-José. An algorithm for computing generalized Hamming weights and the Sage package GHWs. ACM Transactions on Mathematical Software (2025). [preprint] [paper] [GitHub]
9. E. Camps-Moreno, H.H. López, G.L. Matthews, R. San-José. The weight hierarchy of decreasing norm-trace codes. Des. Codes Cryptogr. 93, 2873-2894 (2025). [preprint] [paper]
8. R. San-José. About the generalized Hamming weights of matrix-product codes. Comp. Appl. Math. 44, 186 (2025). [preprint] [paper]
7. D. Ruano, R. San-José. Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem. Journal of Algebra and its Applications (2025). [preprint] [paper]
6. R. San-José. A recursive construction for projective Reed-Muller codes. IEEE Transactions on Information Theory. Volume 70, Issue 12, pages 8511-8523 (2024). [preprint] [paper]
5. D. Ruano, R. San-José. Hulls of projective Reed-Muller codes over the projective plane. SIAM Journal on Applied Algebra and Geometry. Volume 8, Issue 4, pages 846-876 (2024). [preprint] [paper]
4. E. Camps-Moreno, H.H. López, G.L. Matthews, D. Ruano, R. San-José, I. Soprunov. An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance. Quantum Inf. Process. 23, 230 (2024). [GitHub] [preprint] [paper]
3. P. Gimenez, D. Ruano, R. San-José. Subfield subcodes of projective Reed-Muller codes. Finite Fields Appl. 94, 102353 (2024). [preprint] [paper]
2. P. Gimenez, D. Ruano, R. San-José. Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes. Comp. Appl. Math. 42, 363 (2023). [preprint] [paper]
1. P. Gimenez, D. Ruano, R. San-José. Saturation and vanishing ideals. São Paulo J. Math. Sci., 17, 147-155 (2023). [preprint] [paper]

1. E. Camps-Moreno, H.H. López, G.L. Matthews, D. Ruano, R. San-José, I. Soprunov. Binary Triorthogonal and CSS-T Codes for Quantum Error Correction. 60th Annual Allerton Conference on Communication, Control, and Computing (2024). [preprint] [paper]

5. C. Carvalho, H.H. López, R. San-José. Cartesian square-free codes. ArXiv 2511.08304 (2025). [preprint]
4. J. Nardi, R. San-José. Maximum number of zeroes of polynomials on weighted projective spaces over a finite field. ArXiv 2507.22597 (2025). [preprint]
3. O. Campion, R. San-José. Hermitian hull of some GRS codes and new entanglement-assisted quantum MDS codes. ArXiv 2507.18361 (2025). [preprint]
2. E. Camps-Moreno, A. Fidalgo-Díaz, H.H. López, U. Martínez-Peñas, D. Ruano, R. San-José. Duals of multiplicity codes. ArXiv 2505.14472 (2025). [preprint]
1. R. San-José. Recursive decoding of projective Reed-Muller codes. ArXiv 2501.01692 (2025). [preprint]

30. "Maximum number of zeros of polynomials on weighted projective spaces, Part 2", Applied Algebra Seminar, Virginia Tech, Blacksburg. 16/10/2025.
29. "Maximum number of zeros of polynomials on weighted projective spaces, Part 1", Applied Algebra Seminar, Virginia Tech, Blacksburg. 09/10/2025.
28. "Evaluation codes and zeros of polynomials", Colloquium for postdoc appreciation week, Virginia Tech, Blacksburg. 20/09/2025.
27. "Brouwer-Zimmermann algorithm", Graduate Workshop on Linear Algebra over Finite Fields & Applications, ICERM, Brown University. Providence. 28/08/2025.
26. "Generalized Hamming Weights of Decreasing Norm-Trace Codes", SIAM Conference on Applied Algebraic Geometry. Madison. 11/07/2025.
25. "Generalized Hamming Weights of Decreasing Norm-Trace Codes", 2025 Workshop in Coding Theory & Cryptography. Riva San Vitale. 03/07/2025.
24. "The weight hierarchy of decreasing norm-trace codes", 2025 Algebraic Applications to Coding Theory and Crypto workshop. Mexico City. 27/03/25.
23. "Generalized Hamming weights of decreasing codes", Seminar on Algebraic Geometry and Singularities, SINGACOM. Valladolid. 07/03/25.
22. "Using classical codes for quantum fault-tolerant computing", RSME's 7th Congress of Young Researchers. Bilbao. 16/01/25.
21. "Quantum fault-tolerance via classical codes", MatSI, IMAC and Singacom Day on Algebraic Applications to Information Theory. Universitat Jaume I. 16/10/24.
20. "Transversal implementation of non-Clifford gates for quantum fault tolerant computation", Follow-up workshop, Q-CAYLE project. University of Valladolid. 10/10/24.
19. "Bounds for the generalized Hamming weights of projective Reed-Muller codes and matrix-product codes", IIT Bombay - Virginia Tech Joint Workshop on Algebraic Coding Theory. 23/08/24.
18. "Algebraic coding theory and quantum codes", VT-Swiss Coding Theory & Cryptography Summer School. 02/07/24.
17. "A characterization of binary CSS-T quantum codes", IMUVa's PhD day. 27/06/24.
16. "About the hulls of projective Reed-Muller codes", EACA 2024. San Lorenzo del Escorial. 24/06/24.
15. "CSS-T codes from cyclic codes for fault tolerant computation", V MatSI network meeting 2024. Universidad de Alicante. 06/06/24.
14. "Projective Reed-Muller codes: subfield subcodes, generalized Hamming weights and hulls", Séminaire Géométrie et algèbre effectives. Institut de recherche mathématique de Rennes. 09/02/24.
13. "A recursive construction for projective Reed-Muller codes", RSME's Biennial Congress. Pamplona. 25/01/24.
12. "Quantum codes for fault-tolerant computation", Follow-up workshop secureCAT project. Aguilar de Campoo. 11/01/24.
11. "Subfield subcodes of projective Reed-Solomon codes", SIAM TX-LA 2023. University of Louisiana, Lafayette. 04/11/23.
10. "A recursive construction for projective Reed-Muller codes, Part 2", Applied Algebra Seminar, Virginia Tech, Blacksburg. 17/10/23.
9. "A recursive construction for projective Reed-Muller codes, Part 1", Applied Algebra Seminar, Virginia Tech, Blacksburg. 12/10/23.
8. "Vanishing ideals and evaluation codes", ACA 2023. Instytut Informatyki Technicznej, Warsaw. 17/07/23.
7. "Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes", IMUVa's PhD day. 28/06/23.
6. "Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes", PICS. 11/05/23.
5. "Subfield subcodes of projective Reed-Muller codes", RSME's 6th Congress of Young Researchers. Universidad de León. 09/02/23.
4. "Codes over the projective space and applications", Kick-Off Meeting secureCAT project. Aguilar de Campoo. 25/01/23.
3. "About the computation of vanishing ideals with applications to coding theory", Fourth BYMAT Conference. Universitat de València and Universitat Politècnica de València (online). 11/11/22.
2. "Saturation and vanishing ideals", IMUVa's PhD day. 30/06/22.
1. "Saturation and vanishing ideals", XVII Meeting on Computer Algebra and Applications. EACA 2022. Universidad Jaume I de Castellón. 22/06/22.

PhD in Mathematics (thesis), 2021-2024
University of Valladolid

Master's degree in Mathematics, 2020-2021
University of Valladolid

Degree in Mathematics, 2015-2020
University of Valladolid

Degree in Physics, 2015-2020
University of Valladolid