Kaon production in Au+Au collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:mn>6</mml:mn><mml:mi>A</mml:mi><mml:mi> </mml:mi><mml:mi mathvariant="normal">GeV</mml:mi><mml:mo>/</mml:mo><mml:mi>c</mml:mi></mml:math>

A systematic study of the spectra and yields of ${K}^{+}$ and ${K}^{\ensuremath{-}}$ is reported by experiment E866 as a function of centrality in Au+Au collisions at $11.6A \mathrm{GeV}/c.$ The invariant transverse spectra for both kaon species are well described by exponentials in ${m}_{t},$ 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 ${K}^{\ensuremath{-}}$ spectra. The kaon rapidity density peaks at midrapidity with the ${K}^{+}$ distribution wider in rapidity than ${K}^{\ensuremath{-}}.$ The integrated total yields of ${K}^{+}$ and ${K}^{\ensuremath{-}}$ 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 $N\ensuremath{-}N$ 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 ${K}^{\ensuremath{-}}$ rapidity distributions and transverse spectra are consistent with a lower phase space for ${K}^{\ensuremath{-}}$ production due to a higher energy threshold. These differences also exclude simple thermal models that assume emission from a common equilibrated system.