DC10 CREW LOST COM WITH ZKC WHICH RESULTED IN LESS THAN LEGAL SEPARATION WITH ANOTHER ACFT.

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FROM OUR VIEWPOINT; THE FLT PROCEEDED UNEVENTFULLY FROM TKOF TO LNDG. WE WERE CHKING IN WITH EACH ATC FACILITY AND SWITCHING FREQS NORMALLY. THE FO AND SO WERE ON HEADSET; AND THE CAPT HAD THE OVERHEAD SPEAKER TURNED UP. (THE CAPT'S COM SYS HAD BEEN PREVIOUSLY WRITTEN UP FOR PROBS XMITTING.) WE NEVER RECEIVED ANY WORD FROM ANY ATC FACILITY THAT SOMETHING WAS ABNORMAL. HOWEVER; THE NEXT MORNING; OUR COMPANY ADVISED US THAT ZKC LOST SEPARATION BTWN US AND ANOTHER FLT. IT SEEMS THE CTLR FAILED TO PROVIDE SUFFICIENT HEADING CHANGES TO THE OTHER ACFT; WITH WHOM HE WAS IN CONTACT. ALTHOUGH ZKC CLAIMS THEY TRIED TO CONTACT US SEVERAL TIMES AS THE CONFLICT DEVELOPED; NONE OF US HEARD THE CALLS. WE HAVE SUBSEQUENTLY BEEN ADVISED BY OUR COMPANY THAT THIS PARTICULAR QUADRANT AND FREQ IN ZKC HAS REPEATEDLY LOST CONTACT WITH ACFT ON OTHER OCCASIONS; SUGGESTING A RADIO 'DEAD ZONE' MAY EXIT IN THE AREA. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CREW WAS CONTACTED BY HIS ACR; AND WAS TOLD THAT ZKC WAS TAKING ENFORCEMENT ACTION AGAINST THE CREW. THE CAPT NOTES THAT HIS ACR AND OTHER ACRS HAVE RPTED COM PROBS ON THE FREQ. HE THINKS THAT THE FREQ IS 135.5 HE RPTS THAT THERE IS A RADIO DEAD SPOT IN THIS AREA.