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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

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Existence of (near) equidistant codewords

$\beta$ cannot be too much larger than $1/2$; namely we must have $\beta \leq k/(2k-2)$. To prove this, identify the $x_i$ with vectors $v_i \in {\bf R}^n$ each of whose coordinates is $1$ or $-1$, an …
Noam D. Elkies's user avatar