Let expp(q) denote the number of times the prime number p appears in the prime factorization of the integer q. The following result is proved: If there is a perfect 1-error correcting code of length n over an alphabet with q symbols then, for every prime number p,expp(1+n(q-1)) ≤expp(q)(1+(n-1)q). This condition is stronger than both the packing condition and the necessary condition given by the Lloyd theorem, as it for example excludes the existence of a perfect code with the parameters (n,q,e)=(19,6,1).
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