First find the scancode of the key that needs to be remapped, e.g. with the evtest utility. A line like the following one (with MSC_SCAN in it) should be output:
Event: time 1417131619.686259, type 4 (EV_MSC), code 4 (MSC_SCAN), value 70068
followed by a second one giving the current key code. If no MSC_SCAN line is output, this is due to a kernel driver bug, but the scancode can still be found with the input-kbd utility; evtest should have given the key code, so that it should be easy to find the corresponding line in the input-kbd output (e.g. by using grep).
Once the scancodes of the keys to be remapped have been determined, create a file such as /etc/udev/hwdb.d/98-custom-keyboard.hwdb containing the remappings. The beginning of the file /lib/udev/hwdb.d/60-keyboard.hwdb gives some information. In my case (which works), I have:
evdev:input:b0003v05ACp0221*
KEYBOARD_KEY_70035=102nd # Left to z: backslash bar
KEYBOARD_KEY_70064=grave # Left to 1: grave notsign
KEYBOARD_KEY_70068=insert # F13: Insert
(Before udev 220, I had to use keyboard:usb:v05ACp0221* for the first line.)
The evdev: string must be at the beginning of the line.
Note that the letters in the vendor and product id should be capital letters.
Each KEYBOARD_KEY_ settings should have exactly one space before (note: a line with no spaces will give an error message, and a line with two spaces were silently ignored with old udev versions). KEYBOARD_KEY_ is followed by the scancode in hexadecimal (like what both evtest and input-kbd give). Valid values could be obtained from either the evtest output or the input-kbd output, or even from the /usr/include/linux/input.h file: for instance, KEY_102ND would give 102nd (by removing KEY_ and converting to lower case), which I used above.
After the file is saved, type:
udevadm hwdb --update
to (re)build the database /etc/udev/hwdb.bin (you can check its timestamp). Then,
udevadm trigger --sysname-match="event*"
will take the new settings into account. You can check with evtest.
In 2014, the released udev had incomplete/buggy information in /lib/udev/hwdb.d/60-keyboard.hwdb, but you can look at the latest development version of the file and/or my bug report and discussion concerning the documentation and spacing issues.
If this doesn't work, the problem might be found after temporarily increasing the log level of udevd with udevadm control (see the udevadm(8) man page for details).
For old udev versions such as 204, this method should still work.
Best Answer
I've created an utility that sends neccesary commands to the keyboard for it to report additional key events:
https://github.com/tuxmark5/ApexCtl