dc.contributor.author | Bergmann, Markus Aleksander | |
dc.date.accessioned | 2023-10-18T23:38:58Z | |
dc.date.available | 2023-10-18T23:38:58Z | |
dc.date.issued | 2023-09-01 | |
dc.date.submitted | 2023-10-18T22:00:04Z | |
dc.identifier.uri | https://hdl.handle.net/11250/3097383 | |
dc.description.abstract | In this thesis, we investigate the possibility of finding new planar functions and corresponding semifields in characteristic 3 by the construction of isotopic semifields from the known families and sporadic instances of planar functions. Using the conditions laid out by Coulter and Henderson, we are able to deduce that a number of the known infinite families can never produce CCZ-inequivalent functions via isotopism. For the remaining families, we computationally investigate the isotopism classes of their instances over finite fields of order 3^n for n ≤ 8. We find previously unknown isotopisms between the semifields corresponding to some of the known planar functions for n = 6 and n = 8. This allows us to refine the known classification of planar functions up to isotopism, and to provide an updated, partial classification up to isotopism over finite fields of order 3^n for n ≤ 8. | |
dc.language.iso | eng | |
dc.publisher | The University of Bergen | |
dc.rights | Copyright the Author. All rights reserved | |
dc.subject | PN | |
dc.subject | Isotopic | |
dc.subject | Planar | |
dc.subject | Semifield | |
dc.subject | Vectorial function | |
dc.title | Computational search for isotopic semifields and planar functions in characteristic 3 | |
dc.type | Master thesis | |
dc.date.updated | 2023-10-18T22:00:04Z | |
dc.rights.holder | Copyright the Author. All rights reserved | |
dc.description.degree | Masteroppgave i informatikk | |
dc.description.localcode | INF399 | |
dc.description.localcode | MAMN-INF | |
dc.description.localcode | MAMN-PROG | |
dc.subject.nus | 754199 | |
fs.subjectcode | INF399 | |
fs.unitcode | 12-12-0 | |