Consider Z4 ({0, 1, 2, 3} mod 4) refers to a set of integers modulo 4, which means that the integers are divided by 4 and the remainder is taken. In this case, the set includes the numbers 0, 1, 2, and 3.
GF(4) stands for Galois Field of order 4, also known as finite field of size 4. It is a mathematical structure used in coding theory, cryptography, and other areas of mathematics.
Z4 is a set of integers modulo 4, while GF(4) is a mathematical structure with addition and multiplication operations defined over the elements 0, 1, α, and α^2, where α is a primitive element. In other words, GF(4) is a finite field built on the set Z4.
GF(4) is closely related to binary numbers because it is a finite field of size 2^2. This means that the elements of GF(4) can be represented using two binary digits, 0 and 1.
GF(4) has various applications in mathematics and computer science, such as coding theory, cryptography, and error-correcting codes. It is also used in the design of digital circuits and data storage systems.