Counting the number of non-isotopic Taniguchi semifields

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489453" target="_blank" >RIV/00216208:11320/24:10489453 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=K-OTSe5sbL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=K-OTSe5sbL</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10623-023-01262-0" target="_blank" >10.1007/s10623-023-01262-0</a>

Result language
angličtina
Original language name
Counting the number of non-isotopic Taniguchi semifields
Original language description
We investigate the isotopy question for Taniguchi semifields. We give a complete characterization when two Taniguchi semifields are isotopic. We further give precise upper and lower bounds for the total number of non-isotopic Taniguchi semifields, proving that there are around p(m+s) non-isotopic Taniguchi semifields of order p(2m) where s is the largest divisor of m with 2 s ? m. This result proves that the family of Taniguchi semifields is (asymptotically) the largest known family of semifields of odd order. The key ingredient of the proofs is a technique to determine isotopy that uses group theory to exploit the existence of certain large subgroups of the autotopism group of a semifield.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-19087S" target="_blank" >GA18-19087S: Cryptography based on Finite Fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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