MLG LNDG ROLL OVERSHOT USEABLE PORTION OF RWY AND ENTERED THE RECENTLY CLOSED PORTION.

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I WAS FLYING THE MD-80 JETLINER INTO DAYTONA BEACH ARPT; FL. THE ARPT AREA WAS CLR AND VISIBILITY WAS EXCELLENT. THE ACTIVE RWYS WERE 25L AND 25R. WE WERE CLRED A VISUAL APCH TO RWY 25R; WHICH IS NORMALLY 7500 FT IN LENGTH. WE WERE CLRED TO LAND BY THE TWR. NO INSTRUCTION WAS GIVEN TO HOLD SHORT OF ANY POINT ON ROLL-OUT. NO INSTRUCTION WAS GIVEN TO EXIT ON ANY SPECIFIC TXWY ON ROLL-OUT. A NORMAL LNDG WAS MADE; ON SPD; APPROX 1000 FT DOWN THE RWY. LIGHT TO MODERATE REVERSE AND BRAKING WAS USED. I ELECTED TO ROLL BEYOND TXWY N2 WHICH IS 6000 FT FROM THE E END OF RWY 25R. THIS NECESSITATED A 180 DEG TURN ON THE RWY; AS THE NEXT TXWY EXIT WAS CLOSED. AS WE ROLLED PAST TXWY N2 AND THE DISPLACED THRESHOLD MARKINGS FOR RWY 7L; TWR INFORMED US THAT WE WERE ENTERING THE 'CLOSED' PORTION OF THE RWY. WE COULD SEE THAT THERE WERE BARRIERS ABOUT 1000 PLUS FT BEYOND THIS POINT; BUT I SAW NO INDICATION OTHER THAN THE COMMENT FROM TWR; THAT I SHOULD CONSIDER THIS PORTION OF THE RWY 'CLOSED.' WE STOPPED ABOUT 100-200 FT BEYOND TXWY N2 AND RECEIVED PERMISSION TO MAKE 180 DEG TURN ON THE RWY AND THEN EXITED ON TXWY N2. EXCEPT FOR THE COMMENT BY THE TWR; ALL WAS NORMAL. WHEN WE BEGAN THE APCH; WE WERE AWARE OF CONSTRUCTION ON THE WESTERN END OF RWY 25R/7L. ARPT REMARKS AND NOTAMS INCLUDED ON OUR FLT PLAN; AS WELL AS THE DAB ATIS; INDICATED THAT; BECAUSE OF THE CONSTRUCTION; THE THRESHOLD FOR RWY 7L WAS DISPLACED 1500 FT AND THAT THEREFORE 6000 FT WAS AVAILABLE FOR LNDG ON 7L. THE INFO ON OUR FLT PLAN AND ON THE ATIS LED US TO BELIEVE THAT; WHILE ONLY 6000 FT WAS AVAILABLE WHEN LNDG E; THERE WAS 7280 FT AVAILABLE FOR LNDG AND ROLL-OUT WHEN LNDG W. I BELIEVE THE INFO WHICH WE RECEIVED FROM OUR ARPT REMARKS; NOTAMS; AND ATIS WAS UNCLR AND DID NOT INDICATE THE CLOSURE OF THE WESTERNMOST 1500 FT OF RWY 25R/7L. I BELIEVE THAT NOTAMS AND ATIS SHOULD BE EXPLICIT WHEN A PORTION OF RWY IS CLOSED. FURTHERMORE; RWY MARKINGS AND BARRIERS SHOULD SHOW THAT THE RWY SECTION IS CLOSED (NOT JUST DISPLACED THRESHOLD MARKINGS.) IN ADDITION; A SIMPLE REMARK FROM TWR REGARDING THE ABRIDGED RWY LENGTH; COULD BE GIVEN WHEN LNDG CLRNC IS GIVEN. I THINK IN THIS PARTICULAR CASE; THE NOTAM AND ATIS INFO WAS UNCLR BECAUSE THE ORIGINAL PLAN FOR DISPLACING THE 7L THRESHOLD AND LEAVING 7280 FT AVAILABLE FOR OTHER THAN A 7L LNDG WAS CHANGED. THEREFORE; RATHER THAN STARTING WITH AN ORIGINAL NOTAM WHICH SAID 'W 1500 FT OF RWY 7L/25R CLOSED;' WE ENDED UP WITH A SERIES OF NOTAMS WHICH BECAME UNCLR IN INTENT.