For the p-biased hypercube, a k-query linearity test works in the 1% regime if and only if k is at least 1 + 1/min{p,1-p}, up to an odd-k boundary case involving cyclic characters.
On approximability of satisfiable k- CSP s: II
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Biased Linearity Testing in the 1% Regime
For the p-biased hypercube, a k-query linearity test works in the 1% regime if and only if k is at least 1 + 1/min{p,1-p}, up to an odd-k boundary case involving cyclic characters.