Finite fields

Finite fields, also known as Galois fields, are algebraic structures that consist of a finite number of elements and possess operations of addition, subtraction, multiplication, and division (excluding division by zero) that satisfy the field properties. A field is defined by the following properties: 1. **Closure**: The set is closed under the operations of addition, subtraction, multiplication, and non-zero division. 2. **Associativity**: Both addition and multiplication are associative.