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

We prove that a class of q-ary dual BCH-codes in characteristic 2 produce caps in AG(4,q). This is the first family of caps of order 3q2 in PG(4,q). 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, the dual Mélas codes.