ECE4253 Digital Communications
	Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Galois Field GF(2) Calculator

Model C-172 POLYNOMIAL CALCULATOR A: B: A + B A - B A × B A / B Discussion  Polynomials  MATLAB

Answer: (division)

 111001011010
-------------- = 10100001, Remainder = 0000
    11010

Polynomial Form

 x11+x10+x9+x6+x4+x3+x
-------------------- =  x7+x5+1, Remainder: 0
       x4+x3+x

Detailed Calculation

            10100001
      --------------
11010 ) 111001011010
        11010
        -----
         01101011010
          11010
          -----
           000011010
               11010
               -----
                0000

MATLAB Example

Calculations in GF(2) are performed by MATLAB functions found within the Communications Toolbox.

>> a = gf( [1 1 1 0 0 1 0 1 1 0 1 0] );

>> b = gf( [1 1 0 1 0] );

>> [q,r] = deconv(a,b) % deconvolution is equivalent to division

q = GF(2) array.

Array elements =

       1      0      1      0      0      0      0      1

r = GF(2) array.

Array elements =

       0