Parameters measuring the size of set families - Combinatorial Parameters

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Hamming Radius

Name: Hamming Radius

Symbol: $\mathrm{B}$

Definition:

The Hamming Radius $B(\mathcal{H})$ of a family $\mathcal{H}$ is the smallest radius of an enclosing Hamming ball, defined as $$ B(\mathcal{H}):= \min{d: \exists T\subset \mathcal{X},\, \forall h\in \mathcal{H},\, |h\Delta T|\le d} $$

Category: Basic

Symmetric: Yes

Monotonic: Yes

P-Monotonic: Yes

Doubly Monotonic: Yes

Strictly Monotonic: No

Values:

Relationships (as Parameter 1):

Relationships (as Parameter 2):