Weights & Code Words of H(4) & H(5)

[RRRonald199]

Homework Statement

The question is as follows:
Give the appearing weights of the generalized Hamming codes H(4) and H(5). Also give the amount of code words per weight.

Homework Equations

The generalized Hammingcode is defined code existing of all h $\in$ F$^{n}_{2}$ which satisfy h . v = 0 for each v as a row of matrix Q. Where Q contains as colums all the possible words in F$^{m}_{2}$ except for the zero word.

The Attempt at a Solution

Obviously this leads to finding the enumerating polynomials of those codes, and maybe use Mac Williams identity along the way. Yet I can't seem to find a way to do this.

 

[Nino MMP]

So is there a direct way to do this, or is there no other solution than to find the enumerating polynomials?