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In this paper, we introduce an ensemble of random codes called weighted nonbinary repeat accumulate (WNRA) codes. The encoder consists of a nonbinary repeater, a weighter, a pseudorandom symbol interleaver and an accumulator over the finite field GF(q). These codes can be decoded in a simple way by applying the sum-product algorithm to their factor graphs over GF(q). The degree distributions and noise thresholds for the codes are also derived. Simulation results show that WNRA codes with proper weighting are superior to binary RA codes on AWGN channels. Furthermore, WNRA codes over GF(2m) can be used as full-rate space-time codes with full diversity in a multiantenna system where m is the number of transmit antennas.