Abstract
Error correcting codes are used to describe explicit collections F k of subsets of {1,2,...; n}, with | F k | > 2 c k · n ( C k > 0), such that for any selections A, B of k 2 and k 1 of members of F k with k 1 + k 2 = k, there are elements in all the members of A and not in the members of B. This settles a problem of Kleitman and Spencer and a similar problem of Kleimman, Shearer and Sturtevant.
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