Data from the MINOS experiment has been used to search for mixing between muon neutrinos and muon antineutrinos using a time-independent Lorentz-violating formalism derived from the Standard-Model Extension (SME). MINOS is uniquely capable of searching for muon neutrino-antineutrino mixing given its long baseline and ability to distinguish between neutrinos and antineutrinos on an event-by-event basis. Neutrino and antineutrino interactions were observed in the MINOS Near and Far Detectors from an exposure of 10.56$times10^{20}$ protons-on-target from the NuMI neutrino-optimized beam. No evidence was found for such transitions and new, highly stringent limits were placed on the SME coefficients governing them. We place the first limits on the SME parameters $(c_{L})^{TT}_{mumu} $ and $(c_{L})^{TT}_{tautau}$ at $-8.4times10^{-23} < (c_{L})^{TT}_{mumu} < 8.0times10^{-23}$ and $-8.0times10^{-23} < (c_{L})^{TT}_{tautau} < 8.4times10^{-23}$, and the worlds best limits on the $tilde{g}^{ZT}_{muoverline{mu}}$ and $tilde{g}^{ZT}_{tauoverline{tau}}$ parameters at $|tilde{g}^{ZT}_{muoverline{mu}}| < 3.3times 10^{-23}$ and $|tilde{g}^{ZT}_{tauoverline{tau}}| < 3.3times 10^{-23}$, all limits quoted at $3sigma$.
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