A319 suffered a tire failure on the right main gear during takeoff.

Narrative

After what seemed a normal takeoff; we where climbing out and informed by ATC that our aircraft or the previous departing aircraft had 'left some tire rubber' on the runway. Since our departure was normal (no vibrations or shaking or noise) we assumed it was another aircraft. To be safe; we prepared for a precautionary landing. After review of the QRH and FOM we decided to configure for landing early. At one point we received an alert that there was a landing gear system disagree. We elected to do a fly-by at low level. Tower stated; 'it appeared to be the outer main right side tire (#4). At this point the main landing gear position was in question. We reviewed the QRH; once again; as we where circling at 7000. At this point we had 3 green down lights and on the ECAM wheels page we had one green and one red down indication; we concluded that Landing Gear Control Interface Unit (LGCIU) 2 was suspect. In any case we requested Runway XX; with a slight crosswind on the upwind good tire. The Captain landed at -200 VSI...very nice and smooth with minimal braking. We then powered off the runway on a taxiway. Nose wheel steering was inoperative. Tire tread separated and may have came in contact with LGCIU 2 micro switch and delivered an erroneous signal to the cockpit. Right hand flap was damaged as well.