On a binary alphabet, these constructs and one named for Golay are the only nontrivial constructs of their type to be “perfect.” For 10 points each:
[10h] Name these eponymous constructs with minimum distance three. An additional parity bit is often added to the (7, 4) (“seven four”) instance of these constructs to enable double-bit error detection.
ANSWER: Hamming codes [prompt on error-correcting codes]
[10m] Error correction methods like Hamming codes cannot enable information transmission faster than the channel capacity according to this father of information theory’s “noisy-channel coding theorem.”
ANSWER: Claude Shannon [accept Shannon’s theorem]
[10e] Shannon defined this information-theoretic quantity to be the negative sum of “p-sub-i log p-sub-i,” in analogy to the Gibbs formula for a thermodynamic quantity of the same name that roughly measures uncertainty or disorder.
ANSWER: entropy [or information entropy; or Shannon entropy; prompt on S]
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