B767-200
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Aircraft Equipment Problem Less Severe
Aircraft Aircraft Damaged
Aircraft
I did the landing with autobrakes 1. It was a normal landing and actually a fairly smooth touchdown I remember. I let the autobrakes and reverse slow us down to 70 kts; after which I started to apply light braking at first; then medium braking to make [the] taxiway after hearing there was traffic on short final. I got below 10 kts and started to make the turn to the right when I felt a little weird vibration and 'shiver' that seemed to be on the left side; but it went away after I made the turn and I never felt anything unusual after that all the way to the blocks. It pulled a little to the left but not anything more than I've experienced with other airplanes during taxi.We were shocked when; after blocking in and opening the door; a mechanic asked if something happened in the flight and then told me we had blown 4 tires. We went down to look and I took some pictures. I talked to two mechanics there; one of which I recognized and who is very experienced. I explained the same as above; and he didn't seem surprised and seemed to imply the tires had already been a bit worn and close to being needed changed anyway.I've never had something like this in my entire career and my First Officer; is a very experienced pilot who was also surprised and never suspected we had blown tires. I have used heavier braking in the past and know what it feels like when the antiskid activates; and I was nowhere close to that here. I actually went back to the cockpit and recorded the brake temps on the left side. They were 0 for tires 1 and 6; and 1 for tires 2 and 5 (similar to right side). The blown tires were 2 and 5. My only thought was that maybe somehow the brakes on the left side locked up momentarily before I made the turn and caused them to skid and blow? I since learned Maintenance found a wiring issue.
B767-200 Captain reported discovering at the gate that 4 tires had failed; possibly related to a fault in the brake system.