THE AIRCRAFT'S RIGHT NOSE LANDING GEAR TIRE TREAD SEPARATED DURING THE TAKEOFF ROLL. THE TREAD SEPARATION RESULTED IN DAMAGE TO THE GROUND SHIFT MECHANISM, NOSE GEAR DOOR, TAXI LIGHT AND THE EE COMPARTMENT DOOR. THE FLIGHT RETURNED TO THE DEPARTURE AIRPORT. DURING THE LANDING ROLL, WITH THE ANTI-SKID "ON", NO BRAKING ACTION WAS AVAILABLE; HOWEVER, THE AIRCRAFT WAS STOPPED BY USING REVERSE THRUST. AN INVESTIGATION REVEALED THAT THE DAMAGED SHIFT MECHANISM RESULTED IN A FAULTY SIGNAL TO THE ANTI-SKID SYSTEM, PLACING THE BRAKE SYSTEM IN AN "AIRBORNE" MODE. AN INSPECTION OF THE TIRE REVEALED THAT A LINER REPAIR HAD BEEN STITCHED INTO PLACE OVER A CUT REGION. THERE WAS EVIDENCE THAT THE CUT OCCURRED FROM A PUNCTURE. AC145-4, "INSPECTION, RETREAD REPAIR, AND ALTERATIONS OF AIRCRAFT TIRES GENERALLY RECOMMENDED AGAINST ANY ATTEMPT TO REPAIR CUTS THROUGH MORE THAN 40% OF THE PLY AND SPECIFICALLY STATES THAT TIRES WITH PUNCTURES ARE NON-REPAIRABLE.