GF(p)

GF(p), or Galois Field of prime order p, is a set of p elements where p is a prime number, equipped with addition and multiplication operations that follow specific rules. In this system, arithmetic wraps around after reaching p, similar to a clock but with numbers from 0 to p-1. For example, in GF(5), adding 3 and 4 results in 2 because (3 + 4) mod 5 equals 2. This structure allows consistent algebraic operations, making GF(p) fundamental in areas like coding theory, cryptography, and error correction. It provides a finite, well-behaved mathematical environment for various applications.