We prove a geometric property of the set A^{−1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new upper bound on |A^{−1}∩B| when A and B are F_q-subspaces of different dimension of a finite field, satisfying a suitable assumption.
Mattarei, S. (2014). A property of the inverse of a subspace of a finite field. FINITE FIELDS AND THEIR APPLICATIONS, 29, 268-274 [10.1016/j.ffa.2014.05.002].
A property of the inverse of a subspace of a finite field
Mattarei, S
2014
Abstract
We prove a geometric property of the set A^{−1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new upper bound on |A^{−1}∩B| when A and B are F_q-subspaces of different dimension of a finite field, satisfying a suitable assumption.
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