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Addition and multiplication table for GF(2²)

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This blog post has moved to https://matthewvaneerde.wordpress.com/2014/01/30/addition-and-multiplication-table-for-gf2/

Comments

  • Anonymous
    January 30, 2014
    Note that the + table for the binary notation is just XOR.

  • Anonymous
    April 30, 2014
    The comment has been removed

  • Anonymous
    April 30, 2014
    Sorry I upset you; can you elaborate?

  • Anonymous
    August 03, 2014
    how to do that multiplication operation?

  • Anonymous
    August 20, 2014
    There are many ways to check that m(x) = x^8 + x^4 + x^3 + x + 1 is irreducible (prime). The one that is probably easiest to understand is as follows: every polynomial is a product of irreducible polynomials, so it suffices to produce a list of irreducible polynomials of degrees 1 up to 4 and to check by polynomial division that none of them divides m(x) without remainder. These polynomials are x, x+1, x^2 + x + 1, x^3 + x + 1, x^3 + x^2 + 1, x^4 + x + 1, x^4 + x^3 + 1 and x^4 + x^3 + x^2 + x + 1. To verify this list, just write all the polynomials up to degree 4 down and check which ones are divisible by a polynomial of smaller degree.

  • Anonymous
    January 02, 2015
    Anyone can tell me How we Construct a Multiplication table of GF(2^3)

  • Anonymous
    January 02, 2015
    The comment has been removed

  • Anonymous
    March 06, 2016
    Cannot understand anything about GF(2^3) from your explanation

    • Anonymous
      March 25, 2017
      multiply both the numbers in their polynomial form,divide by the irreducible polynomialand take the remainder.

  • Anonymous
    May 02, 2016
    TRULY INFORMATIVE SIR.THANKS A LOT.

  • Anonymous
    December 19, 2016
    Very helpful, thank you!