UNAUTH RWY XING ENTRY. RWY INCURSION.

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WE WERE OPERATING INTO PIT APPROX 35 MINS LATE AT NIGHT AT THE END OF AN 11 HR DAY. I BRIEFED A VISUAL APCH TO RWY 28L WITH A PLANNED TURNOFF AT THE HIGHSPD SO AS TO MINIMIZE TAXI TIME TO THE GATE. AFTER LNDG AND EXITING THE HIGHSPD (C3); TWR SAID 'CALLSIGN; STAY WITH ME; R TURN ON C2 TO THE RAMP.' THE FO READ BACK 'R TURN; C2 TO THE RAMP' AND I VERBALIZED THE CLRNC BACK TO HIM; 'R TURN; C2 TO THE RAMP.' I THEN EXECUTED A R TURN ONTO V TXWY (THE RTE I HAD ANTICIPATED WHEN BRIEFING THE APCH) AND EXPECTED TO SEE C2 AS AN ENTRANCE TO THE RAMP AREA UP AHEAD. I THEN SPOTTED ANOTHER ACFT XING R TO L (ON W TXWY) AND CALLED THE FO'S ATTN TO HIM WONDERING OUT LOUD WHY TWR HAD NOT POINTED HIM OUT. TWR THEN INFORMED US THAT WE HAD CROSSED A RWY (28C) WITHOUT PERMISSION. CAUSE OF PROB? MY FAILURE TO BE SURE OF TAXI INSTRUCTIONS PRIOR TO LEAVING C3. TWR SHOULD HAVE SAID 'L ON C; THEN R ON C2 TO THE RAMP.' CONTRIBUTING FACTORS: LONG DAY; RUNNING LATE; NIGHT; NEW TERMINAL; LACK OF FAMILIARITY; SMALL 20- 9 PLATE; DISTRACTED FO FROM LOOKING AT 20-9 BY POINTING OUT XING TFC; BY ANTICIPATING TAXI-IN VIA V (THE SHORTEST RTE); I SET MYSELF UP TO MISINTERPRET THE CTLR'S INSTRUCTIONS.