Bilinear dual hyperovals from binary commutative presemifields II

We construct a bilinear dual hyperoval Sc(S1,S2,S3) from binary commutative presemifields S1=(GF(q),+,∘) and S2=(GF(q),+,⁎), a binary presemifield S3=(GF(q),+,⋆) which may not be commutative, and a non-zero element c∈GF(q) which satisfies some conditions. We also determine the isomorphism problems under the conditions that S1 and S2 are not isotopic, and c≠1. We also investigate farther on the isomorphism problem on the case that S1 and S2 are the Kantor commutative presemifields and S3 is the Albert presemifield.