3 papers
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.NT2025
Proof of the Lehmer conjecture on Ramanujan's function
Minjia Shi, Lu Wang, Patrick Solé
A criterion for Lehmer's conjecture in terms of the spherical designs held in the shells of the lattice was derived by de La Harpe, Pache and Venkov circa 2005. We check that…