Galois field addition and multiplication rule

[Reni Septiana]

I'm just starting to learn about channel coding and it looks like that this topic uses a lot galois field. In all books I've read they only provide addition and multiplication table, but not explain much more. I'm still confused how are actually addition and multiplication rules in galois field?
thx..

 

[LouisSheffield]

I believe it's much like normal polynomial arithmetic, except that all resulting polynomial coefficients are modulo p.

https://en.wikipedia.org/wiki/Finite_field_arithmetic