Hamming Bound

For a q-ary block code of length n with minimum Hamming distance d and unique-decoding radius t = floor((d-1)/2), the Hamming bound (sphere-packing bound in Hamming metric) states that the number of codewords M satisfies M · V_q(n,t) ≤ q^n, where V_q(n,t)=∑_{i=0}^t binom(n,i)(q-1)^i is the volume of a Hamming sphere of radius t.