Hyperovals in Knuth’s binary semifield planes.

In each of the three projective planes coordinatized by the Knuth’s binary semifield K n of order 2 n and two of its Knuth derivatives, we exhibit a new infinite family of 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. [ABSTRACT FROM AUTHOR]