Xbox 360 1080i works but 1080p no , with Samsung 46 series 6 ?

i have a TV Samsung LCD 46 inch series 6 supports full HD 1080p but when i connect my Xbox 360 (special edition 250GB + Kinect) (PAL)
so when i connect the console with the TV and i put resolution 1080i it works properly, but when i turn it to 1080p, the video suffers from things like small white stripes and some grain makes playing on it bad idea
and by the way i use a HDMI cable i bought it by 12$ (3 meters – bandwidth up to 10.2Gbps ) and it is written “supports 1080p”
so where is the real problem ? and what is the solution ?
answer please if you know

i have the exact same problem…. no solution yet…it works 1080p with the component cable

Xbox 360 4GB Console with Kinect $259.99 Microsoft Xbox 360 S4G-00001 Gaming Console with Game Pad S4G-00001 Video Game Consoles…

Xbox 360 250GB Console with Kinect $349.99 Microsoft Xbox 360 S7G-00001 Gaming Console with Kinect – Wireless – Black S7G-00001 Video Game Consoles…

Madden NFL 12 $0.01 …