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This paper introduces blind-channel estimation methods using residue polynomials for orthogonal-frequency-division-multiplexing (OFDM) transmission under the assumption that the channel is finite-impulse response (FIR). In terms of z transform, if the received signal is multiplied by the inverse of the transmitted signal, the resulting z transform renders the channel transfer function when additive noise is absent in the channel. For an FIR channel, samples of the recovered impulse response must be zero in the region of zeros of the channel impulse response. Based on this observation, the blind estimation problem is formulated as a solution of linear equations, treating the transmitted symbols as unknown variables. Polynomial residue arithmetic turns out to be very useful for deriving the linear equations. The proposed method is computationally more efficient than subspace methods that are applied for OFDM transmission systems. In addition, unlike subspace methods, the proposed method is deterministic and does not require estimation of the autocorrelation matrix of received signals, which is required in subspace methods.