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We prove here some dimension free Poincar\'e-type inequalities on Hammingcube for functions with different spectral properties and for fractionalLaplacians. In this note the main attention is paid to estimates in $L^1$ normon Hamming cube. We build the examples showing that our assumptions on spectralproperties of functions cannot be dropped in general.

Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube