A field is a mathematical structure with a lot of useful properties. In general, you can take an arbitrary set and define two binary operators on it. If the set and binary operators satisfy some rather strict requirements, the structure you created is a field. A Galois Field is a specific finite field with specific binary operators that very much resemble addition and multiplication that you are used to, but with some distinct differences. Each Galois Field has a certain size. For example, is typically represented with the elements and the binary operators are modular addition and modular multiplication. However, that is because that set equipped with modular addition and modular multiplication is isomorphic to . Each Galois Field is unique in the sense that any other field of the same size is isomorphic to it. In other words, your field could have elements in it that look nothing like numbers. Your binary operators might not make any sense when related to numbers. But, there is a way to assign numbers to each element of your set so that the binary operators become very similar to addition and multiplication.