Balancing sets of vectors

Constant weight codes: An approach based on Knuth's balancing method

“…Knuth showed that the redundancy p is roughly equal to log 2 m, for m >> 1 [5], [7]. Modifications of the generic scheme are discussed in Knuth [5], Alon et al [8], Al-Bassam & Bose [9], Tallini, Capocelli & Bose [10], and Weber & Immink [7].…”

Extremal Combinatorics

“…, A n be subsets of X. Then the number of elements of X which lie in none of the subsets A i is (19) I⊆{1,...,n} (−1) |I| |A I |.…”

Explicit Constructions

“…As shown by Alon, Bergmann, Coppersmith and Odlyzko (1988), this construction is optimal, i.e., K(n) = n for all even n. Let us sketch the proof of the lower bound. For simplicity, we consider only the case n ≡ 0(mod 4).…”