Generalizes Delsarte bounds to multivariate Q-polynomial association schemes, deriving upper bounds on codes and designs characterized via Wilson polynomials, plus Lloyd-type conditions and applications to Lee distance and orthogonal arrays.
Perfect codes in weakly metric association schemes
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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. 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.
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Codes and designs in multivariate $Q$-polynomial association schemes
Generalizes Delsarte bounds to multivariate Q-polynomial association schemes, deriving upper bounds on codes and designs characterized via Wilson polynomials, plus Lloyd-type conditions and applications to Lee distance and orthogonal arrays.