Binary Cyclic Codes

Determine all binery cyclic codes of length 5.

Note: To find all cyclic codes of length n, find all ideals in B[x]/x^2+1
Note: If 1 is an Ideal (I) then R = I.

Example:
n=2
R=B[x]/x^2+1, x^2=1

R={o,1,x,1+x}

Ideals <0> = 0
          <1> = R
          x = (0, x, x^2...)
                 = (1,...
                 = R
      <1+x> = (1+x, 0, x+x^2, 1+x^2)
      x+x^2 = x+1
      1+x^2 = 1+1 = 0 so,

      <1+x> = (1+x, 0)

Therefore:

Ideal                     Code Words
<0>                      00
<1>                      00
                            01
                            10
                            11
x = <1>
<1+x>                  00
                            11