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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.

2 votes

Existence of (near) equidistant codewords

Following up on Noam's answer: for $k = 3$ I think the bound is even tighter, $\beta \leq 2/3$. If $d(x,y), d(y,z) > n(\frac{2}{3} + \epsilon)$, then if we define $A = \{i \ : \ x_i \neq y_i\}$ and $B …
Ronnie Pavlov's user avatar