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Perfect codes in weakly metric association schemes
[Submitted on 19 Jan 2026 (v1), last revised 9 Sep 2026 (this ve · 2026-01-19 · via math updates on arXiv.org

This paper has been withdrawn by Patrick Solé

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Abstract:The Lloyd Theorem of (Solé, 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.
A connection between this notion and the recent theory of multivariate P-polynomial schemes of ( Bannai et al. 2025) and of $m$-distance regular graphs ( Bernard et al 2025) is pointed out.

Submission history

From: Patrick Solé [view email]
[v1] Mon, 19 Jan 2026 08:24:35 UTC (24 KB)
[v2] Mon, 1 Jun 2026 11:15:45 UTC (24 KB)
[v3] Wed, 9 Sep 2026 01:16:59 UTC (1 KB) (withdrawn)