the Schwartz-Zippel Lemma
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Perfect codes in weakly metric association schemes
Announce Type: replace-cross Abstract: The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank distance. The proofs are based on asymptotic enumeration of integer partitions. The framework is the new concept of {\em polynomial} weakly metric association schemes.