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perfect codes

perfect codes Error-correcting codes in which the Hamming spheres surrounding the codewords entirely fill the Hamming space without overlap. These spheres all have radius e, where the code can correct e errors, and their centers (codewords) are separated from each other by a distance of (2e + 1); thus the spheres have no points (words) in common where they touch, but their surfaces are separated by unit distance with no points between them. Perfect codes attain the Hamming bound exactly.

The only binary linear perfect codes are the repetition codes, the Hamming codes, and the (23,12) Golay code.

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