An extremal problem for integer sparse recovery

04/18/2019

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by   Sergei Konyagin, et al.

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Motivated by the problem of integer sparse recovery we study the following question. Let A be an m × d integer matrix whose entries are in absolute value at most k. How large can be d=d(m,k) if all m × m submatrices of A are non-degenerate? We obtain new upper and lower bounds on d and answer a special case of the problem by Brass, Moser and Pach on covering m-dimensional k ×...× k grid by linear subspaces.