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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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Minimally intersecting subsets of fixed size
maybe you would be interested in the "Minimal Overlapping Algorithm" presented in "Two New Combinatorial Problems involving
Dominating Sets for Lottery Schemes - Werner R Grundlingh" (at page 155):
T …