14 high-impact publications and 5 theses defended in the fields of cryptography and quantum computing.
The project’s research team has made significant progress in the field of error-correcting codes and cryptography, sharing the technical knowledge generated with the international scientific community. This effort strengthens national R&D in cybersecurity and gives the results of the PECIEE project high visibility.
Doctoral theses defended as part of the project:
- “Quantum Algorithms for Algebraic Structures” (2024),
- by Miguel Hernández Cáceres.
"Decoding Group Codes" (2025),
by Fabián Ricardo Molina Gómez.
"Group Codes in Cryptography" (2026),
by Beatriz García García.
- “Quantum computing models for algebraic structures via abstract detection systems” (2025), by Guillermo Lugilde Fernández.
- “Algebraic and formal techniques for the analysis of quantum algorithms” (2026), by Samuel González Castillo.
Notable publications
Papers have been published in high-impact international journals and leading conference proceedings, including:
- Finite Fields and Their Applications (2 articles, 2025): “On the square code of group codes” (Alejandro Piñera Nicolás, Ignacio Fernández Rúa, Adriana Suárez Corona) Finite Fields and Their Applications 103 (2025) 102548 ; “Decoding algorithms in group codes” (Consuelo Martínez, Fabián Molina, Alejandro Piñera Nicolás) *Finite Fields and Their Applications* 108 (2025) 102692
- Journal of Algebra and Its Applications (1 article, 2026): “Permutation decoding in group codes” (Consuelo Martínez, Fabián Molina) Journal of Algebra and Its Applications (2027) 2750136 DOI: 10.1142/S0219498827501362
- Entropy (1 Open Access article, 2026): “Cyclicity of Binary Group Codes” ( Beatriz García García, Consuelo Martínez López, Ignacio Fernández Rúa) Entropy (2026)
* Proceedings of the RECSI (2 articles in 2024 and 2 in 2026): “Classification of binary group codes of length less than 24” (Beatriz García García, Ignacio Fernández Rúa); “Permutation decoding in group codes” (Fabián Molina); “A study of the cyclicity of binary group codes over non-Abelian groups of order less than 24” (Beatriz García García, Consuelo Martínez López, Ignacio Fernández Rúa); “LDOI Group Codes with a Binary Adjacency Matrix” (Fabián Molina, Consuelo Martínez)
- Mathematical Methods in the Applied Sciences (1 article, 2025): “General Gate Teleportation and the Inner Structure of Its Clifford Hierarchies” (Samuel González Castillo, Elías Fernández-Combarro, Ignacio Fernández Rúa, José Ranilla) Mathematical Methods in the Applied Sciences, 2025;0:1–13 1
* Quantum Information Processing (1 article, 2026): “On finding PUBO problems on Diophantine equations” (Miguel Hernández Cáceres, Ignacio Fernández Rúa) Quantum Information Processing 25:113
* 4 preprints submitted for peer review.
Participation in leading conferences
The team has actively disseminated its results to researchers, the academic community and companies in the cryptography sector through presentations at leading events:
- RECSI 2024 (León) and RECSI 2026 (La Laguna).
- CB-Crypto 2025 (Madrid).
- RSME conferences (Young Researchers 2025, Bilbao, and Biennial 2026, Alicante).
- UAX International Cybersecurity Conference (Madrid, 2025)
* or Quantum Technology International Conference (QTech 2024, Berlin)
o Quantum Technologies for Young Researchers workshop (QTYR25, Madrid)
o 25th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2025, Rota)
