On maximal curves with Frobenius dimension 3

Frobenius dimension is one of the most important birational invariants of maximal curves. In this paper, a characterization of maximal curves with Frobenius dimension equal to 3 is provided. Our main tool is the Natural Embedding Theorem for maximal curves. As an application, maximal curves with Frobenius dimension 3 defined over the fields with 16 and 25 elements are completely classified.

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