I am trying to find all binary cyclic codes with parameters $\left[21,12\right]$.
From my work so far, I have found that for $\left[21,12\right]$ cyclic codes there are seven generator polynomials,
$x^9+x^3+1$
$x^9+x^6+1$
$x^9+x^8+x^7+x^2+x+1$
$x^9+x^8+x^5+x^4+x^2+x+1$
$x^9+x^8+x^7+x^5+x^4+x+1$
$x^9+x^7+x^6+x^5+x^3+x^2+x+1$
$x^9+x^8+x^7+x^6+x^4+x^3+x^2+1$
and that each of these makes a $\left[21,12\right]$ code with respective distance 3, 3, 5, 4, 5, 4, 4. This leads me to conclude that there are seven such codes.
However, the problem I am running into is that Appendix D, from Error Correcting Codes by Peterson and Weldon, states that there are four such codes, $\left[21,12,3\right], \left[21,12,4\right], \left[21,12,4\right]$ and $\left[21,12,5\right]$. Clearly I am either failing to understand something, or the text is wrong, and I'm certain it's the former.
Why does the text state that there are only four such codes when I have found seven? Why does the text include a repeat while excluding other repeats? I verified my results from pen and paper calculations with matlab, and I just can't figure out what I am failing to grasp. Any help would be greatly appreciated.