Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09068 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914796564119552 |
|---|---|
| author | Kölsch, Lukas |
| author_facet | Kölsch, Lukas |
| contents | In this article, we present two new constructions for semifields of order $p^{2m}$. Together, the constructions unify and generalize around a dozen distinct semifield constructions, including both the oldest known construction by Dickson and the largest known construction in odd characteristic by Taniguchi. The constructions also provably yield many new semifields. We give precise conditions when the new semifields we find are equivalent and count precisely how many new inequivalent semifields we construct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unifying construction of semifields of order $p^{2m}$ Kölsch, Lukas Combinatorics Rings and Algebras In this article, we present two new constructions for semifields of order $p^{2m}$. Together, the constructions unify and generalize around a dozen distinct semifield constructions, including both the oldest known construction by Dickson and the largest known construction in odd characteristic by Taniguchi. The constructions also provably yield many new semifields. We give precise conditions when the new semifields we find are equivalent and count precisely how many new inequivalent semifields we construct. |
| title | A unifying construction of semifields of order $p^{2m}$ |
| topic | Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2405.09068 |