Start by reading the Derivative Distro Howto.
You can certainly make a distribution based on Ubuntu, and as far as I know there is no specific restriction on the live CD, so you can make derivative works based on it.
The code isn't be a problem: as far as I know it's all freely redistribuable software, Ubuntu doesn't have any specific rights to distribute that you don't also have. But the branding — trademarks and artwork — might be. The obvious thing you should check is what you may do with the Ubuntu artwork, and how you're allowed to use the name (it's trademarked).
A typical example of artwork and trademark-related limitation is the Iceweasel saga. The Mozilla foundation wants only “acceptable” derivatives of Firefox to have the Firefox brand, so even though the software is free software (as in free speech), the branding is not. Although the Mozilla foundation was prepared to trust Debian to make only acceptable changes, such as security fixes, they were not willing to extend that trust to others. But the Debian Free Software Guidelines specify that the “license must not be specific to Debian”, so that people in your position know that they can make derivatives. Since no acceptable compromise was found, Debian does not distribute “Firefox”, it distributes “Iceweasel” with the same code and different branding.
Ubuntu is less strict on that point, so if you want to make a derivative, you do have to check whether you may retain the branding on any component you change (starting with the distribution as a whole).