A systematic study of the spectra and yields of K+ and K− is reported by experiment E866 as a function of centrality in Au+Au collisions at 11.6A GeV/c. The invariant transverse spectra for both kaon species are well described by exponentials in mt, with inverse slope parameters that are largest at midrapidity and which increase with centrality. The inverse slopes of the K+ spectra are slightly larger than the inverse slopes of the K− spectra. The kaon rapidity density peaks at midrapidity with the K+ distribution wider in rapidity than K−. The integrated total yields of K+ and K− increase nonlinearly and steadily with the number of projectile participants. The yield per participant for kaons is two to three times larger than the yield from N−N collisions. This enhancement suggests that the majority of kaons in central Au+Au reactions are produced in secondary hadronic collisions. There is no evidence for an onset of additional kaon production from a possible small volume of baryon-rich quark-gluon plasma. The differences between K+ and K− rapidity distributions and transverse spectra are consistent with a lower phase space for K− production due to a higher energy threshold. These differences also exclude simple thermal models that assume emission from a common equilibrated system.
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