We consider the transmission and storage of data that use coded binary symbols over a channel, where a Pearsondistance-based detector is used for achieving resilience against additive noise, unknown channel gain, and varying offset. We study Minimum Pearson Distance (MPD) detection in conjunction with a set, S, of codewords satisfying a center-of-mass constraint. We investigate the properties of the codewords in S, compute the size of S, and derive its redundancy for asymptotically large values of the codeword length n. The redundancy of S is approximately 3/2 log2 n + α where α = log2 √π/24 =-1.467. for n odd and α =-0.467. for n even. We describe a simple encoding algorithm whose redundancy equals 2 log2 n + o(log n). We also compute the word error rate of the MPD detector when the channel is corrupted with additive Gaussian noise.