Abstract
In this article we use pairs of Dembowski–Ostrom polynomials with special properties (see (P1)–(P3) in the introduction below) to construct translation planes of order q n which admit cyclic groups of order q n −1 having orbits of lengths 1, 1, (q n −1)/2, (q n −1)/2 on the line at infinity. The same pairs also define semifields of order q 2n . We discuss the properties of these translation planes and semifields. These constructions extend the related construction in Dempwolff and Muller, Osaka J Math [5].
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