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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 3/2024

02-07-2023

Counting the number of non-isotopic Taniguchi semifields

Authors: Faruk Göloğlu, Lukas Kölsch

Published in: Designs, Codes and Cryptography | Issue 3/2024

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Abstract

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 \(2\,s\ne m\). 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.
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Metadata
Title
Counting the number of non-isotopic Taniguchi semifields
Authors
Faruk Göloğlu
Lukas Kölsch
Publication date
02-07-2023
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 3/2024
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-023-01262-0

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