Hamming Bound - Statement of The Bound

Statement of The Bound

Let denote the maximum possible size of a -ary block code of length and minimum Hamming distance (a -ary block code of length is a subset of the strings of where the alphabet set has elements).

Then, the Hamming bound is:

\ A_q(n,d) \leq \frac{q^n}{\sum_{k=0}^t \binom{n}{k}(q-1)^k}

where

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