Evasive subspaces

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Abstract

Abstract Let denote an ‐dimensional vector space over , the finite field of elements. Then is also an ‐dimension vector space over . An ‐subspace of is ‐evasive if it meets the ‐dimensional ‐subspaces of in ‐subspaces of dimension at most . The ‐evasive subspaces are known as scattered and they have been intensively studied in finite geometry, their maximum size has been proved to be when is even or . We investigate the maximum size of ‐evasive subspaces, study two duality relations among them and provide various constructions. In particular, we present the first examples, for infinitely many values of , of maximum scattered subspaces when and . We obtain these examples in characteristics 2, 3 and 5.

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