Konečná polotělesa, samoopravné kódy a kryptografie

• Thesis title in Czech: Konečná polotělesa, samoopravné kódy a kryptografie
• Thesis title in English: Finite semifields, error-correcting codes and cryptography
• Academic year of topic announcement: 2024/2025
• Thesis type: dissertation
• Thesis language: čeština
• Department: Department of Algebra (32-KA)
• Supervisor: doc. Faruk Göloglu, Dr. rer. nat.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 13.02.2025
• Date of assignment: 13.02.2025
• Confirmed by Study dept. on: 13.02.2025

Guidelines

The thesis will contain original research on a combination of
(1) certain algebraic and combinatorial aspects of finite semifields
such as isotopy invariants, constructions, enumerations, solutions of
quadratic and higher degree equations over finite semifields, etc.,
(2) applications in coding theory, especially in the case of MRD
(Maximum Rank Distance) codes, and
(3) applications in cryptography via code-based cryptography similar
to McEliece (a variant of which is currently a contender in the
NIST competition for Post-Quantum Cryptography).

References

[1] Lavrauw, Michel and Polverino, Olga.
Finite semifields.
In Storme, Leo and De Beule, Jan, editor, Current research topics in Galois geometry,
Mathematics Research Developments, pages 127–155. Nova Science, 2011.

[2] Johnson, Norman L.; Jha, Vikram; Biliotti, Mauro.
Handbook of finite translation planes.
Pure Appl. Math. (Boca Raton), 289 Chapman & Hall/CRC, Boca Raton, FL, 2007.

[3] Sheekey, John.
MRD codes: constructions and connections
Radon Ser. Comput. Appl. Math., 23
De Gruyter, Berlin, 2019, 255–285.