Author

Heng-Jia Wei

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Preprint Aug 2026

The Optimal Asymptotic Rate of Generalized Covering Codes

Let $G_q$ be an alphabet of size $q\geq2$. We determine the optimal asymptotic rate of generalized covering codes $C\subseteq G_q^n$, whose covering centers in $G_q^{t\times n}$ are constrained to the product form $C^t$. For every fixed integer $t\geq1$ and every $\rho\in[0,1]$, we prove that \[ \kappa_t(\rho,q)= \begi...

Heng Li, Chong Shangguan, Heng-Jia Wei · 3 citations

Preprint Sep 2026

Random Algebraic Geometry Codes Approach the Half-Singleton Bound for Insertions and Deletions

It is demonstrated that curves with many rational points allow for nearly optimal codes over significantly smaller alphabets, and the existence of random AG codes that approach the half-Singleton bound with high probability over fields of size, breaking the linear field size barrier.

Zhi-Hao Guan, Heng-Jia Wei · 0 citations