# Introductory Explanation for Carry-less and Galois Field arithmetic
There are three completely separate types of Galois-Field-based
-arithmetic that we implement which are not well explained even in introductory
-literature. These are:
+arithmetic that we implement which are not well explained even in introductory literature. A slightly oversimplified explanation
+is followed by more accurate descriptions:
* carry-less binary arithmetic. this is not actually a Galois Field,
but is accidentally referred to as GF(2) - see below as to why.
* modulo arithmetic with a Prime number, these are "proper" Galois Fields
* modulo arithmetic with two limits: a power-of-2 (2^N) and a second
- "reducing" polynomial (with characteristics similar to a prime number)
+ "reducing" polynomial (similar to a prime number)
-further detailed explanations are provided below
+further detailed and more precise explanations are provided below
## Polynomials with coefficients in `GF(2)`