Abstract:
It is shown that the length of a nontrivial perfect code over the Galois field $GF(q)$ correcting $t\geqslant8$ errors is strictly bounded on both sides. This result implies that for values of $q=2,3,4,5,7$ and 8 nontrivial perfect codes other than the already known Hamming and Golay codes are nonexistent.
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