Bilinear dual hyperovals from binary commutative presemifields II

We construct a bilinear dual hyperoval S-c(S-1, S-2, S-3) from binary commutative presemifields S-1 = (GF(q),+,o) and S-2 = (G F (q), +, *), a binary presemifield S-3 = (G F (q), +, *) which may not be commutative, and a non-zero element c is an element of GF(q) which satisfies some conditions. We also determine the isomorphism problems under the conditions that Si and S-2 are not isotopic, and c not equal 1. We also investigate farther on the isomorphism problem on the case that S-1 and S-2 are the Kantor commutative presemifields and S-3 is the Albert presemifield. (C) 2017 Elsevier Inc. All rights reserved.