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The theory of error-correcting codes stems from Shannon's 1948 _A mathematical theory of communication_, and from Hamming's 1950 "Error detecting and error correcting codes".

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covering by spherical caps

Consider the unit sphere $\mathbb{S}^d.$ Pick now some $\alpha$ (I am thinking of $\alpha \ll 1,$ but I don't know how germane this is). The question is: how many spherical caps of angular radius $\al …