Software was only a minor issue
The biggest issue was mounting the engines forward and up on the wing. This created an instability where the plane would pitch up when accelerating. Rather than add training of the pilots they decided to hide the problem by installing the software solution. They then fscked up the implementation in several ways and the rest is, unfortunately, history and about 300 dead people.
The airframe should have been recertified, they did all this to avoid having to do it.
Andy