The novel class of nonbinary maximum minimum distance redundant residue number system (RRNS) codes is invoked in the context of adaptively RRNS coded, symbol-by-symbol adaptive multicarrier modulation, in order to combat the effects of frequency-selective fading inflicted by dispersive wide-band channels. The system's performance can be adjusted in order to maintain a given target bit error rate (BER) and bit per symbol (BPS) performance. The proposed adaptive RRNS scheme outperforms the convolutional constituent code based turbo coded benchmarker system for channel signal-to-noise ratios (SNR) in excess of about 15 dB at a target BER of 10/sup -4/.