Lower Bounds
نویسنده
چکیده
Proof. We induct on d. Exercise 1 proved the base case d = 1. Consider d ≥ 2 and a d-disjunct matrix M with t = t(d,N) rows and N columns. Let N(w) denote the number of columns of M with weight w. (The weight of a column is the number of 1s in it.) A row i ∈ [t] is said to be private for a column j if j is the only column in the matrix having a 1 on row i. If column Mj has weight at most d, then it must have at least one private element. The total number of private elements of all columns is at most t. Hence,
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