  Charged kaon production has been measured in Si+Al and Si+Au collisions at
14.6 A GeV/c, and Au+Au collisions at 11.1 A GeV/c by Experiments 859 and 866
(the E--802 Collaboration) at the BNL AGS. Invariant transverse mass spectra
and rapidity distributions for both K+ and K- are presented. The centrality
dependence of rapidity-integrated kaon yields is studied. Strangeness
enhancement is observed as an increase in the slope of the kaon yield with the
total number of participants as well as the yield per participant. The
enhancement starts with peripheral Si+Al and Si+Au collisions (relative to N+N)
and appears to saturate for a moderate number of participating nucleons in
Si+Au collisions. It is also observed to increase slowly with centrality in
Au+Au collisions, to a level in the most central Au+Au collisions that is
greater than that found in central Si+A collisions. The enhancement factor for
$K^+$ production are 3.0 +-0.2(stat.) +-0.4(syst.) and 4.0 +-0.3(stat.)
+-0.5(syst.), respectively, for the most central 7% Si+Au collisions and the
most central 4% Au+Au collisions relative to N+N at the correponding beam
energy.
