A property of the inverse of a subspace of a finite field
Abstract
We prove a geometric property of the set A-1 of inverses of the nonzero elements of an Fq-subspace A of a finite field involving the size of its intersection with two-dimensional Fq-subspaces. We give some applications, including a new upper bound on the size of the intersection of A-1 and B when A and B are Fq-subspaces of different dimension of a finite field, satisfying a suitable natural assumption.
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