Reinstall software-center in Ubuntu 16.04
Solution 1:
I know this is an old question, but here's the thing: the software center is not named software center. It's named ubuntu-software. I didn't reinstall through terminal, I used Synaptic, but I think you could probably reinstall by
sudo apt install --reinstall ubuntu-software
Also, you don't need apt-get in 16.04. You just need the apt.
Solution 2:
I believe the Ubuntu Software Centre was replaced by the GNOME Software Centre in the new Ubuntu update.
To install the new GNOME software centre try the following commands:
sudo add-apt-repository ppa:ubuntu-desktop/gnome-software
sudo apt-get update
sudo apt-get install gnome-software packagekit