We derive a recursive formula determing the weight distribution of the [n=(q^m-1)/(q-1), n-m, 3] Hamming code H(m,q), when (m, q-1)=1. Here q is a prime power. The proof is based on Moisio's idea of using Pless power moment identity together with exponential sum techniques.
Cite
@article{arxiv.0710.1467,
title = {Weight Distributions of Hamming Codes},
author = {Dae San Kim},
journal= {arXiv preprint arXiv:0710.1467},
year = {2007}
}