# Rank and fooling set size

@article{Hamed2013RankAF, title={Rank and fooling set size}, author={Aya Hamed and Troy Lee}, journal={ArXiv}, year={2013}, volume={abs/1310.7321} }

Say that A is a Hadamard factorization of the identity I_n of size n if the entrywise product of A and the transpose of A is I_n. It can be easily seen that the rank of any Hadamard factorization of the identity must be at least sqrt{n}. Dietzfelbinger et al. raised the question if this bound can be achieved, and showed a boolean Hadamard factorization of the identity of rank n^{0.792}. More recently, Klauck and Wolf gave a construction of Hadamard factorizations of the identity of rank n^{0… CONTINUE READING

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