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Upper bounds are derived on the number of codewords in error-correcting (d,k)-constrained block codes. The author focuses on simple error-correcting schemes, such as single-error correction, since the recording channels on which these codes are used usually have a very low bit error rate. Multierror-correcting codes with a relatively short block length are not practical, since a high code rate is a major concern. The notation of a (d,k)-constrained block code is discussed. The concept of combined codes is introduced, several bounds are derived, and several examples are given.