English

Hyperovals in Knuth's binary semifield planes

Combinatorics 2016-05-23 v1

Abstract

In each of the three projective planes coordinatised by the Knuth's binary semifield Kn\mathbb{K}_n of order 2n2^n and two of its Knuth derivatives, we exhibit a new family of infinitely many translation hyperovals. In particular, when n=5n=5, we also present complete lists of all translation hyperovals in them. The properties of some designs associated with these hyperovals are also studied.

Keywords

Cite

@article{arxiv.1605.06267,
  title  = {Hyperovals in Knuth's binary semifield planes},
  author = {Nicola Durante and Rocco Trombetti and Yue Zhou},
  journal= {arXiv preprint arXiv:1605.06267},
  year   = {2016}
}
R2 v1 2026-06-22T14:05:27.670Z