It's easy, all you do is call EA and press the numbers accordingly to what they say, I believe BF3 issues is number 1.

When you get to an operator (Warning: Waiting times are ridiculous) simply say your copy of limited edition didn't come with a code or say the code that came with it doesnt work. They'lll ask you for your GT, Email, and name and after that they just send one to your email. It's as easy as that