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Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.
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Minimize average bitwise entropy with given pairwise hamming distance
First decompose the total distance $D$ by component: $$D = \sum_{i,j\in [n]} d(a_i,a_j) = \sum_{l \in [m]} \sum_{i,j\in [n]} \mathbf{1}\{a_{il} \neq a_{jl}\}.$$ Let $\delta_l = \frac{1}{n^2} \sum_{i,j …