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This paper considers using BCH codes for distributed source coding using feedback. The focus is on coding using short block lengths for a binary source, X, having a high correlation between each symbol to be coded and a side information, Y, such that the marginal probability of each symbol, Xi in X, given Y is highly skewed. In the analysis, noiseless feedback and noiseless communication are assumed. A rate-adaptive BCH code is presented and applied to distributed source coding. Simulation results for a fixed error probability show that rate-adaptive BCH achieves better performance than LDPCA (Low-Density Parity-Check Accumulate) codes for high correlation between source symbols and the side information.