Generating orthomorphisms of GF(q)+

Abstract A map θ : GF( q ) + →GF( q ) + , with O θ =0, is an orthomorphism of GF( q ) + if θ and the map η defined by xη = xθ − x are both bijections. Orthomorphisms can be used in the construction of sets of mutually orthogonal latin squares and in the construction of affine planes. In this paper we give a method for constructing classes of orthomorphisms of GF( q ) + . We also described all orthomorphisms of GF( q ) + for q ⩽ 8.

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