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In this letter, we propose a new forward error correction (FEC) coding method using a coset constructed from a bent function and a Reed-Muller (RM) code for providing accurate dimming control in on-off keying-based visible light communication (VLC) systems. By partitioning the coset made from bent function and the first-order RM codes, the new FEC scheme can be made to be suitable for dimming close to 0% or 100%. Therefore, it can contain minimal compensation symbols in supporting multiple dimming target values, which causes improved coding gain when the total amount of frame data is fixed. Simulation results for various dimming target values show that the proposed scheme leads to about 1-dB signal-to-noise ratio gain in 10-2 bit error rate compared with other three FEC codes.