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 interests are algebraic coding theory and quantum error correction. I am also interested in their connections with commutative algebra, algebraic geometry, and cryptography.
Here are some quotes that I like or find funny. You can also check out my tier list of books that I like.

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

My full name is Rodrigo San José Rubio.

14. O. Campion, R. San-José. Hermitian hull of some GRS codes and new entanglement-assisted quantum MDS codes. Quantum Inf. Process. 25, 277 (2026).
13. J. Nardi, R. San-José. Maximum number of zeroes of polynomials on weighted projective spaces over a finite field. Bull. London Math. Soc., 58: e70417 (2026).
12. R. San-José. Recursive decoding of projective Reed-Muller codes. IEEE Transactions on Information Theory. Volume 72, Issue 5, pages 2769-2779 (2026).
11. E. Camps-Moreno, A. Fidalgo-Díaz, H.H. López, U. Martínez-Peñas, D. Ruano, R. San-José. Duals of multiplicity codes. Des. Codes Cryptogr. 94, 81 (2026).
10. R. San-José. An algorithm for computing generalized Hamming weights and the Sage package GHWs. ACM Trans. Math. Softw., 51(4) (2025).
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).
8. R. San-José. About the generalized Hamming weights of matrix-product codes. Comp. Appl. Math. 44, 186 (2025).
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, 24(13n14):2541009 (2025).
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).
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).
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).
3. P. Gimenez, D. Ruano, R. San-José. Subfield subcodes of projective Reed-Muller codes. Finite Fields Appl. 94, 102353 (2024).
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).
1. P. Gimenez, D. Ruano, R. San-José. Saturation and vanishing ideals. São Paulo J. Math. Sci., 17, 147-155 (2023).

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).

6. R. San-José. Wei-type duality and asymptotics of the footprint bound. ArXiv 2607.10680 (2026).
5. H.H. López, R. San-José, N. Shalqini. Reed-Muller type codes over a combinatorial simplex: an algebraic description. ArXiv 2606.02819 (2026).
4. D. Jaramillo-Velez, H.H. López, R. San-José. Private neighbors, perfect codes, and their relation with the v-number of closed neighborhood ideals. ArXiv 2603.28247 (2026).
3. J. Nardi, R. San-José. Structure of weighted projective Reed-Muller codes. ArXiv 2603.24397 (2026).
2. E. Camps-Moreno, H.H. López, G.L. Matthews, N. Rengaswamy, R. San-José. Transversal gates for quantum CSS codes. ArXiv 2601.21514 (2026).
1. C. Carvalho, H.H. López, R. San-José. Cartesian square-free codes. ArXiv 2511.08304 (2025).

35. "A Serre-like bound for weighted projective spaces", 2026 Workshop in Coding Theory & Cryptography. Riva San Vitale. 29/06/26.
34. "Zeros of polynomials on weighted projective spaces", Conference in Honor of Rafael H. Villarreal on the Occasion of his 75th Birthday, Cinvestav, Mexico City. 09/06/26.
33. "Relative generalized Hamming weights and their applications in cryptography", ILAS 2026, Virginia Tech, Blacksburg. 21/05/26.
32. "Transversal diagonal logical gates of CSS codes", Workshop: Combinatorial coding theory, AIM, Pasadena. 17/04/26.
31. "Recursive decoding of projective Reed-Muller codes", Final workshop ANR BARRACUDA, CIRM, Marseille. 05/01/26.
30. "Maximum number of zeros of polynomials on weighted projective spaces, Part 2", Applied Algebra Seminar, Virginia Tech, Blacksburg. 16/10/25.
29. "Maximum number of zeros of polynomials on weighted projective spaces, Part 1", Applied Algebra Seminar, Virginia Tech, Blacksburg. 09/10/25.
28. "Evaluation codes and zeros of polynomials", Colloquium for postdoc appreciation week, Virginia Tech, Blacksburg. 20/09/25.
27. "Brouwer-Zimmermann algorithm", Graduate Workshop on Linear Algebra over Finite Fields & Applications, ICERM, Brown University. Providence. 28/08/25.
26. "Generalized Hamming Weights of Decreasing Norm-Trace Codes", SIAM Conference on Applied Algebraic Geometry. Madison. 11/07/25.
25. "Generalized Hamming Weights of Decreasing Norm-Trace Codes", 2025 Workshop in Coding Theory & Cryptography. Riva San Vitale. 03/07/25.
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