High precision measurements of a weak interaction decay were conducted to search for possible variation of the decay rate parameter caused by an antineutrino flux. The experiment searched for variation of the ⁵⁴Mn electron capture decay rate parameter to a level of precision of 1 part in ∼10⁵ by comparing the difference between the decay rate in the presence of an antineutrino flux ∼3×10¹² cm^-2sec^-1 and no flux measurements. The experiment is located 6.5 meters from the reactor core of the High Flux Isotope Reactor (HFIR) in Oak Ridge National Laboratory. A measurement to this level of precision requires a detailed understanding of both systematic and statistical errors. Otherwise, systematic errors in the measurement may mimic fundamental interactions. <div><br></div><div>The gamma spectrum has been collected from the electron capture decay of ⁵⁴Mn. What differs in this experiment compared to previous experiments are, (1) a strong, uniform, highly controlled, and repeatable source of antineutrino flux, using a reactor, nearly 50 times higher than the solar neutrino flux on the Earth, (2) the variation of the antineutrino flux from HFIR is 600 times higher than the variation in the solar neutrino flux on the Earth, (3) the extensive use of neutron and gamma-ray shielding around the detectors, (4) a controlled environment for the detector including a fixed temperature, a nitrogen atmosphere, and stable power supplies, (5) the use of precision High Purity Germanium (HPGe) detectors and finally, (6) accurate time stamping of all experimental runs. By using accurate detector energy calibrations, electronic dead time corrections, background corrections, and pile-up corrections, the measured variation in the ⁵⁴Mn decay rate parameter is found to be δλ/λ=(0.034±1.38)×10^-5. This measurement in the presence of the HFIR flux is equivalent to a cross-section of σ=(0.097±1.24)×10^-25cm². These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a 68% confidence level upper limit sensitivity in δλ/λ <= 1.43×10^-5 or σ<=1.34×10^-25cm² in cross-section. The cross-section upper limit obtained in this null or no observable effect experiment is ∼10⁴ times more sensitive than past experiments reporting positive results in ⁵⁴Mn.</div>