TRACON ARTS RADAR DOES A DATA TAG SWAP WHICH CAUSES A LTSS OCCURRENCE.

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AFTER TAKING OFF FROM RWY 28R AT PDX DEP CTL ISSUED A TURN TO 160 HDG. WE WERE ALREADY CLRED TO 9000 FT (THIS TURN SEEMED REASONABLE ACCOUNT RWY 28L WAS CLOSED). SOON; 3 THINGS HAPPENED AT ONCE: 1) WE CAME ON TOP OF AN OVCST; 2) DEP ISSUED AN URGENT LEVEL-OFF AT 3000 FT; 3) THE TCASII GAVE AN RA OF DSND-DSND. WE FOLLOWED THE TCASII COMMAND AND OBSERVED THE CONFLICTING TFC -- WHICH WAS THE SMT WHICH DEPARTED IFR JUST BEFORE WE DID. APPARENTLY (LEARNED FROM A SERIES OF LATER PHONE CALLS). OUR RADAR TAG ATTACHED ITSELF TO ANOTHER JET DEP ABOUT 8 MI IN FRONT OF US -- THE TURN TO 160 HDG WAS REALLY FOR HIM. THE TCASII SAVED THE DAY AND A VERY ALERT CTLR WAS SECONDS BEHIND THE TCASII -- BUT PROBABLY WOULD HAVE BEEN TOO LATE. I DON'T UNDERSTAND THE TECHNICALITIES; BUT CONTRIBUTING TO THE ERROR WAS THE FACT THAT BOTH ACFT (JETS) HAD XPONDER CODES A FEW DIGITS APART. IF XPONDER CODES WERE ASSIGNED TRULY AT RANDOM; THE CHANCES OF MY TYPE OF INCIDENT COULD BE REDUCED. MAYBE NASA COULD LOOK INTO HOW XPONDER CODES ARE ASSIGNED AND FIND A METHOD WHICH TAKES ADVANTAGE OF TRUE RANDOM ASSIGNMENTS.