[Galaxy Tab 3 Q&A, Help & Troubleshooting] Restl3ss:
64 bit is more than just file names, there's also a lot to do with memory management. There's also 64-bit only applications

the kernel source and toolchain you should be able to find at the tab 3 development by learning developers thread, for toolchain though you can pretty much just use the same things you would for a standard cm11 compilation

so if you're on a 32 bit system,

apt-get install bison build-essential curl flex git gnupg gperf libesd0-dev libncurses5-dev libsdl1.2-dev libwxgtk2.8-dev libxml2 libxml2-utils lzop openjdk-6-jdk openjdk-6-jre phablet-tools pngcrush schedtool squashfs-tools xsltproc zip zlib1g-dev

and if you're on a 64 bit system it's the same as above + a few extras, so

apt-get install bison build-essential curl flex git gnupg gperf libesd0-dev libncurses5-dev libsdl1.2-dev libwxgtk2.8-dev libxml2 libxml2-utils lzop openjdk-6-jdk openjdk-6-jre phablet-tools pngcrush schedtool squashfs-tools xsltproc zip zlib1g-dev g++-multilib gcc-multilib lib32ncurses5-dev lib32readline-gplv2-dev lib32z1-dev

if you're running a debian distro (such as kali) you're gonna want to add a couple repos to sources.list.

gedit /etc/apt/sources.list

and add the following lines (one might already be there, if so just skip adding that one. duplicate lines cause problems)

deb http://ftp.de.debian.org/debian sid main
deb http://ftp.ca.debian.org/debian/ wheezy main

take note that if you're running a debian distro the package phablet-tools listed above won't be installable through apt-get. so install every other package listed above with apt-get install, then for phablet tools you're gonna have to grab the .deb + its dependancies and install it manually. once phablet tools is installed along with the rest of the above run apt-get install on all of them just to make sure they all say the newest version is already installed. If done correctly you now have your toolchain. do a reboot via the terminal.

Take note that installing these packages on a debian installation WILL break your GUI (i've tested this in 3 different distros, always happens) so when you boot up after installing the above tools you'll just have a command line. Dont worry. Log in as root and type

apt-get -o=APT::Force-LoopBreak install kde-full

let that run its course then once it's finished reboot from the console. when you boot up again you should have your GUI back (though maybe not the one you had initially. This will function just as well though)

if after the reboot you find yourself back into the console, log in and type "startx". if that doesnt work, type "startkde". KDE should boot automatically but occasionally it goes back to console, one of those two is guarinteed to boot your GUI.

If for some reason when trying to log into KDE it just boots back into the login screen, hit the button in the lower left pannel of the login window next to power and switch it to "failsafe". Login like normal, you'll get a terminal window. (xserver is running but the gui is not fully) type "startx" or "startkde" in this window. Try them in that order. One of them will boot KDE like normal.

If all went well, bam, you're in your desktop and you've got your toolchain.

(I seriously recommend debian for building. Significantly more difficult to set up but ubuntu has a platoon of problems with the brunch command)

I know that was fairly long winded haha, but that should give you everything you need. If you get gedit isnt installed at any point just grab it with

apt-get install gedit

also, I highly recommend building from source for a device or two that already has CM available before you try to build based on angel_666's thread. it's best you're comfortable with the process, as working a port is a lot more intensive. Adding some unmerged gerrit code and rebuilding will also make you more comfortable with the source file structure.

also, keep me updated on kali mini if you don't mind, I'm intrigued :p