How to rebind keys to key combinations?

I really would like to switch to Linux, but there is still this one last thing I just can't get working. On Windows I'm using autohotkey to rebind some keys to key combinations, and I'm just too used to it to use the system without it.

I'm using the following bindings:

LAlt + j = LeftArrow LAlt + k = Enter LAlt + l = RightArrow LAlt + i = UpArrow LAlt + , = DownArrow LAlt + Shift + j = Ctrl + LeftArrow LAlt + Shift + k = Shift + Enter LAlt + Shift + l = Ctrl + RightArrow LAlt + p = Backspace LAlt + [ = Delete LAlt + Shift + p = Ctrl + Backspace LAlt + Shift + [ = Ctrl + Delete LAlt + c = copy LAlt + x = cut LAlt + v = paste 

I have tried using the Linux equivalent of autohotkey - Autokey, but it's too high level to be usable, even in Firefox up and down arrows won't work like they should.

I have also tried xmodmap, but it seems to be impossible to achieve my bindings with it.

Any suggestions?

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