Caps of order 3q² in affine 4-space in characteristic 2

Finite Fields and Their Applications, 10 (2004), 168-182.

doi:10.1016/S1071-5797(03)00050-9

Abstract:

For q=2^f, f odd, we prove that a class of q-ary dual BCH-codes produce (3q²+4)-caps. This is the first family of caps of order 3q² in PG(4,q). They are in fact affine. It is proved that our caps are complete in PG(4,q). We determine the weight distribution of the codes generated by the caps, via a close link to the binary Kloosterman codes.

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