Consider Z4 ({0, 1, 2, 3} mod 4) and GF (4) (also known as GF(2^2)).

  • Thread starter krispiekr3am
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In summary, Consider Z4 ({0, 1, 2, 3} mod 4) is a set of integers divided by 4 with the remainder taken, including the numbers 0, 1, 2, and 3. GF(4) is a Galois Field of order 4, a mathematical structure used in coding theory, cryptography, and other areas. The difference between Z4 and GF(4) is that GF(4) is a finite field built on the set Z4. GF(4) is closely related to binary numbers as it is a finite field of size 2^2. It has various applications in mathematics and computer science, including coding theory, cryptography, and data storage
  • #1
krispiekr3am
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(a) Is (Z4, +) a group? Is (Z4, +, *) a ring? Explain.
(b) Is Z4 a field, in other words, does every integer in Z4 have a multiplicative inverse?
(c) Generate the addition table and multiplication table of GF(4).

can someone help me. i am clueless?
 
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  • #2
Have you had any thoughts on the problem?
 
  • #3
In particular, have you written out the addition and multiplication tables for Z4?
 

Related to Consider Z4 ({0, 1, 2, 3} mod 4) and GF (4) (also known as GF(2^2)).

1. What is Consider Z4 ({0, 1, 2, 3} mod 4)?

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.

2. What is GF(4)?

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.

3. What is the difference between Z4 and GF(4)?

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.

4. How is GF(4) related to binary numbers?

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.

5. What are the applications of GF(4)?

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.

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