Hyperovals in Knuth's binary semifield planes

2016/05/20 by Nicola Durante, Durante, Nicola, Rocco Trombetti +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1605.06267

arxiv created 2016/05/20 · openalex publication_date 2016/05/20 · arxiv updated 2016/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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