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In this paper we introduce a notion to be called k-wise uncorrelated random variables, which is similar but not identical to the so-called k-wise independent random variables in the literature. We show how to construct k-wise uncorrelated random variables by a simple procedure. The constructed random variables can be applied, e.g. to express the quartic polynomial (x T Qx) 2 , where Q is an n × n positive semidefinite matrix, by a sum of fourth powered polynomial terms, known as Hilbert'sdoi:10.1287/moor.2013.0626 fatcat:nz5ofrfv3bflxlujhje7wpbrdu