The calibration and performance of the opposite-side flavour tagging algorithms used for the measurements of time-dependent asymmetries at the LHCb experiment are described. The algorithms have been developed using simulated events and optimized and calibrated with B+ -> J/psi K+, B0 -> J/psi K*0 and B0 -> D*- mu+ nu_mu decay modes with 0.37 fb^-1 of data collected in pp collisions at sqrt(s) = 7 TeV during the 2011 physics run. The opposite-side tagging power is determined in the B+ -> J/psi K+ channel to be (2.10 +- 0.08 +- 0.24) %, where the first uncertainty is statistical and the second is systematic.
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