GF(p) stands for Galois Field of prime order p. It is a mathematical structure used in various fields such as coding theory and cryptography. In GF(p), the elements are integers from 0 to p-1, and arithmetic operations like addition and multiplication are performed modulo p. This means that when the result of an operation exceeds p-1, it wraps around to start from 0 again. The properties of GF(p) make it particularly useful for constructing error-correcting codes and secure communication systems. Each element in the field has a unique additive and multiplicative inverse, allowing for well-defined operations. This structure is foundational in many areas of modern mathematics and computer science.