Semifields and skew polynomial rings
| Thesis title in Czech: | Polotělesa a okruhy kosých polynomů |
|---|---|
| Thesis title in English: | Semifields and skew polynomial rings |
| Key words: | okruh kosých polynomů|Oreho rozšíření|polotěleso|MRD kód |
| English key words: | skew polynomial ring|Ore extension|semifield|MRD code |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| 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: | 07.03.2023 |
| Date of assignment: | 07.03.2023 |
| Confirmed by Study dept. on: | 03.04.2023 |
| Date and time of defence: | 12.09.2023 10:00 |
| Date of electronic submission: | 19.07.2023 |
| Date of submission of printed version: | 24.07.2023 |
| Date of proceeded defence: | 12.09.2023 |
| Opponents: | Mgr. Jiří Pavlů |
| Guidelines |
| The objective of this thesis is to explain semifields arising from skew polynomial rings [1,2].
The thesis should explain the notion of cyclic semifields and its correspondence to the construction from skew polynomial rings [2]. Also relevant is the so-called MRD-codes which can be seen as a generalization of semifields. These objects should be explained in the context of the paper [1] which also contains constructions of further semifields. |
| References |
| [1] Sheekey, John: New semifields and new MRD codes from skew polynomial rings. J. Lond. Math. Soc. (2) 101 (2020), no. 1, 432–456.
[2] Lavrauw, Michel; Sheekey, John: Semifields from skew polynomial rings. Adv. Geom. 13 (2013), no. 4, 583–604. |