Singleton bound

In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code ${\displaystyle C}$ with block length ${\displaystyle n}$, size ${\displaystyle M}$ and minimum distance ${\displaystyle d}$.

The minimum distance of a set ${\displaystyle C}$ of codewords of length ${\displaystyle n}$ is defined as

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