A BE40 CAPT; PF; ADMITTED THAT HE MISUNDERSTOOD HIS CLRNC WHILE ON APCH TO MSY; CAUSING HIM TO TRIGGER A LOW ALT WARNING IN THE TWR.

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MY FO AND I WERE ON AN IFR FLT TO MSY. WE WERE VECTORED FOR THE LOC RWY 19 AT MSY AND CLRED FOR THE APCH AND TOLD TO MAINTAIN 2000 FT MSL UNTIL JASPO. THE WX WAS VMC AND I BRIEFED THE APCH QUICKLY. IN THE FMS WE HAD JOCIE; JASPO AND THE MAP DISPLAYED ON THE MOVING MAP DISPLAY ON THE MFD. I WAS BTWN JOCIE AND JASPO AND STARTED MY DSCNT DOWN TO 700 FT MSL; WHICH WAS DEFINITELY INCORRECT. I WAS NOT SUPPOSED TO DSND UNTIL REACHING JASPO. FOR SOME REASON I WAS THINKING JOCIE WAS JASPO; AND THE MISSED APCH WAS SHORE. AS I WAS SAYING; APCH CTL CHANGED ME OVER TO TWR. I CALLED TWR; AND HE CLRED ME TO LAND. I THEN STARTED MY DSCNT AND AT APPROX 1200 FT MSL TWR ISSUED ME A LOW ALT ALERT. HE TOLD ME THAT I WAS SUPPOSED TO STAY AT 2000 FT MSL UNTIL JASPO; WHICH IS CORRECT. I REALIZED WHAT HAD HAPPENED AND LEVELED OFF MY DSCNT. BOTH MYSELF AND MY FO GOT JOCIE AND JASPO CONFUSED. I WAS IN VMC THE ENTIRE TIME; AND I DID WONDER WHY IT LOOKED LIKE I WAS SO LOW SO FAR FROM THE ARPT. LOOKING BACK; I THINK THAT WE SHOULD HAVE BRIEFED THE APCH MORE CAREFULLY. I RAN THROUGH THE BRIEFING QUICKLY BECAUSE THE WX WAS NOT BAD; AND WE WERE LOOKING AT SOME TSTMS JUST NW OF THE ARPT. THIS WAS JUST A FUEL STOP ENRTE TO MCALLEN; TX. THE TWR NEVER HAD US CALL OR SAID ANYTHING ELSE OF THE INCIDENT. ANOTHER THING THAT COULD MAKE A DIFFERENCE WOULD BE TO NOT HAVE CONSECUTIVE INTXNS STARTING WITH THE SAME LETTER; AND OUR MFD DID NOT DISPLAY SHORE INTXN. THIS IS A GOOD REMINDER THAT WE NEED TO BRIEF OUR APCHS MORE CLOSELY; AND TAKE TIME TO SEE WHAT IS IN THE FMS; AND WHAT IS DISPLAYED ON THE MFD.