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In this letter, we propose a novel forward error correction (FEC) coding method using a modified Reed-Muller (RM) code for providing accurate dimming control in on-off keying (OOK) based visible light communication (VLC) systems. The proposed FEC scheme has a property that produces exactly same occurrence probability of 1's and 0's. Therefore, it can contain minimal compensation symbols in supporting multiple dimming target values. Moreover, VLC with our proposed scheme provides more coding gain than VLC scheme with the conventional FEC codes [the first-order RM and Reed-Solomon (RS) codes]. Simulation results for various dimming target values show that the proposed scheme leads to at least 2 dB or more signal-to-noise ratio (SNR) gain in 1% bit error rate (BER) than two FEC codes.