Linux: can't recognize the combination Ctl and letter, like Ctl+K Ctl+J

Question

Trying to set Ctl+J Ctl+K to Up/Down as I used to do, using xdotool key Up/Down.

But setting the shortcut in gnome keyboard properties or in compiz manager doens't work. you can set it to F6 for example but not Ctl+J.

Vim interestingly can't map C-S to save file. it does however map C-I for the same purpose however.

I wonder if there is any place where these keys are mapped to something else and preventing global mapping.