High Quality Content by WIKIPEDIA articles! Let C be a q-ary code of length n, i.e. a subset of [q]n. Let R be the rate of C and ? be the relative distance. In coding theory, the Singleton bound, named after R.C. Singleton, is a relatively crude bound on the size of a block code C with block length n, size r and minimum distance d. First observe that there are qn many q-ary words of length n, since each letter in such a word may take one of q different values, independently of the remaining letters. Now let C be an arbitrary q-ary block code of minimum distance d. Clearly, all codewords c in C are distinct. If we delete the first d ? 1 letters of each codeword, then all resulting codewords must still be pairwise different, since all original codewords in C have Hamming distance at least d from each other. Thus the size of the code remains unchanged.

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