Sphere Packing Bound
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The sphere packing bound is a theorem suggesting the largest grouping of codes where no overlap exists.
$|C| \le \frac{2^n}{\displaystyle\sum_{i=0}^t {n \choose i}}$
- When $d$ is odd, $d = 2t - 1$
- When $d$ is even, $d = 2t - 2$
To maximise the number of codewords $|C|$ we want to minimise the error detection capability $t$. This will consequently affect the minimum distance $d(C)$ / minimum weight $w(C)$.
Conversely if we minimise $d$, we maximise $|C|$