Precise predictions for an $e^+e^-rightarrow tbar{t}$ cross-section are presented in the energy region from 400 GeV to 800 GeV. Cross-sections are estimated including the beam-polarization effects with full $mathcal{O}(alpha)$, and also with the effects of the initial-state photon emission. A radiator technique is used for the initial-state photon emission up to two-loop orders. In this investigation, a weak correction is defined as the full electroweak corrections without the initial-state photonic corrections. As a result, it is determined that the total cross-section of a top quark pair-production receives the weak corrections of $+4%$ over the trivial initial state corrections at a center of mass energy of 500 GeV. Among the initial state contributions, a contribution from two-loop diagrams gives less than $0.11%$ correction over the one-loop ones at the center of mass energies of from $400$ GeV to $800$ GeV. In addition, the effect of a running coupling constant is also discussed.
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