Kódy hodnostní metriky

• Thesis title in Czech: Kódy hodnostní metriky
• Thesis title in English: Rank-metric codes
• Key words: linearizované polynomy|hodnostní metrika|kódy nejvzdálenější hodnosti|Gabidulinovy kódy
• English key words: linearized polynomials|rank metric|maximum rank distance codes|Gabidulin codes
• Academic year of topic announcement: 2023/2024
• Thesis type: Bachelor's thesis
• Thesis language: angličtina
• Department: Department of Algebra (32-KA)
• Supervisor: doc. Faruk Göloglu, Dr. rer. nat.
• Author: Bc. Adam Burda - assigned and confirmed by the Study Dept.
• Date of registration: 15.03.2024
• Date of assignment: 15.03.2024
• Confirmed by Study dept. on: 21.05.2024
• Date and time of defence: 12.09.2024 10:00
• Date of electronic submission: 09.05.2024
• Date of submission of printed version: 09.05.2024
• Date of proceeded defence: 12.09.2024
• Opponents: doc. Mgr. et Mgr. Jan Žemlička, Ph.D.

Guidelines

The thesis is on constructions of rank-metric codes. It should explain
the rank metric first and then give main constructions due to Delsarte
and Gabidulin using [Chapter 2, 1] and some quite recent ones such as
in [2,3] and expand the explanations whenever necessary. Then $q$-cyclic
codes [Chapter 3, 1] and its generalizations [4,5] should be explained.
These are related to skew-polynomial rings which will be explained as
well.

References

[1] Ernst M. Gabidulin, "Rank Codes", TUM.University Press, 2021.
[2] J. Sheekey, “A new family of linear maximum rank distance codes,” Advances in Mathematics of Communications, vol. 10, pp. 475–488, 2016.
[3] K. Otal and F. Özbudak, “Additive rank metric codes,” IEEE Transactions on Information Theory, vol. 63, no. 1, pp. 164–168, 2017.
[4] D. Boucher and F. Ulmer, “Coding with skew polynomial rings,” Journal of Symbolic Computation, vol. 44, no. 12, pp. 1644–1656, 2009.