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A product construction for perfect codes over arbitrary alphabets (Corresp.)

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A general product construction for perfect single-error-correcting codes over an arbitrary alphabet is presented. Given perfect single-error-correcting codes of lengths n, m , and q + 1 over an alphabet of order q , one can construct perfect single-error-correcting codes of length (q - 1)nm + n + m over the same alphabet. Moreover, if there exists a perfect single-error-correcting code of length q + 1 over an alphabet of order q , then there exist perfect single-error-correcting codes of length n , n = (q^{t} _ 1)/(q - 1) , and (t > 0 , an integer). Finally, connections between projective planes of order q and perfect codes of length q + 1 over an alphabet of order q are discussed.

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Information Theory, IEEE Transactions on  (Volume:30 ,  Issue: 5 )