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math.CO2026
Perfect codes in weakly metric association schemes
Minjia Shi, Jing Wang, Patrick Solé
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, N…
math.CO2026
Codes and designs in multivariate -polynomial association schemes
Minjia Shi, Jing Wang, Patrick Solé +1
We generalize the fundamental bounds of Delsarte thesis (1973) on codes of given degree and designs of given strength in the new setting of Bannai et al. (2025). We assume the sche…
math.CO2026
The punctured dodecacode is unique
Markus Grassl, Denis Krotov, Lin Sok +1
The punctured dodecacode is an additive -ary code of length and distance which is uniformly packed. We show that a code with the same weight distribution is equivalent…