Functions on the half-slice passing the k-query BLR test with probability (1+δ)/2 agree with an affine function on (1 + δ^{1/(k-2)})/2 - o(1) fraction of points, for k≥3.
Direct Sum Testing
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Low Soundness Linearity Testing on the Half-Slice
Functions on the half-slice passing the k-query BLR test with probability (1+δ)/2 agree with an affine function on (1 + δ^{1/(k-2)})/2 - o(1) fraction of points, for k≥3.