There are two well-known necessary conditions for the existence of a perfect error-correcting code. Combination of these leads to a Diophantine equation. It is proved that this equation has no solutions for n > 2, q > 3 (q a prime power) in the case of two errors. Furthermore we prove that the Golay (23, 12) code is the only nontrivial perfect 3-error-correcting code over any alphabet GF(q).
Published
1970
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