On minimal subspace Zp-null designs

11/30/2020

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by   Denis S. Krotov, et al.

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Let q be a power of a prime p, and let V be an n-dimensional space over the field GF(q). A Z_p-valued function C on the set of k-dimensional subspaces of V is called a k-uniform Z_p-null design of strength t if for every t-dimensional subspace y of V the sum of C over the k-dimensional superspaces of y equals 0. For q=p=2 and 0≤ t<k<n, we prove that the minimum number of non-zeros of a non-void k-uniform Z_p-null design of strength t equals 2^t+1. For q>2, we give lower and upper bounds for that number.