Here is more information since I am not sure what to change in what you have given above to accomodate for it. I will be using this LFSR to encrypt text. This text will be encoded over $Z_128$ (assuming a change is needed for this?) and the LFSR will need to work with the binary representation of the text. (which I think is ok already)

@kguler I found my mistake. I was using append instead of appendto in some spots. It works now. Thanks!

It is giving me errors though, I will show those in my edit now.

I actually turned them into lists, so it is currently a list of lists like {{0,0,0,1},{0,0,0,1}}

Could you look at my edit please. I am confused on the issue

Expanded on the acronym. Thanks

Thanks for pointing me into the correct direction with Module. Could you check my edit and tell me if it is the way others would expect the function to look.

My mistake, thank you for pointing this out.