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The error-correcting codes for symbols from GF (2b) are often used for correction of byte-errors in binary data. In these byte-error-correcting codes each check symbol in GF (2b) is expressed as b binary check digits and each information symbol in GF (2b), likewise, is expressed by b binary information digits. A new class of codes for single-byte-error correction is presented. The code is general in that the code structure does not depend on symbols from GF (2b). In particular, the number of check bits are not restricted to the multiples of b as in the case of the codes derived from GF (2b) codes. The new codes are either perfect or maximal and are easily implementable using shift registers.