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New families of complete caps in finite Galois spaces are obtained. For most pairs [ABSTRACT FROM AUTHOR]

The Hurwitz bound on the size of the -automorphism group Aut() of an algebraic curve  of genus g ≥ 2 defined over a field  of zero characteristic is |Aut()| ≤ 84(g − 1). For a positive characteristic, algebraic curves can have many more automorphisms than expected from the Hurwitz bound. There even exist algebraic curves of arbitrary high genus g with more than 16g4 automorphisms. It has been observed on many occasions that the most anomalous examples of algebraic curves with very large automorphism groups invariably have zero p-rank. In this paper, the -automorphism group Aut() of a zero 2-rank algebraic curve  defined over an algebraically closed field  of characteristic 2 is investigated. The main result is that, if the curve has genus g ≥ 2 and |Aut()| > 24g(g − 1), then Aut() has a fixed point on , apart from a few exceptions. In the exceptional cases, the possibilities for Aut() and g are determined. [ABSTRACT FROM PUBLISHER]