Year: 2026
Type: preprint
Abstract: We study the maximal length of MDS algebraic geometry codes from genus-two curves over finite fields. Let $C_\mathcal{ L}(D,G)$ be such a code over $\mathbb F_q$, with length $n$ and dimension $k$. Assume that $3\leq k\leq n-3$. We prove that $n<(2q+10\sqrt q+16)/3$. This bound holds for every prime power $q$ and for both parities of $k$. It gives a uniform upper bound of $2q/3+O(\sqrt q)$ for the maximal length. The explicit bound is strictly smaller than $q+1$ when $q\geq125$.
Source: arXiv (Cornell University)
Author: Chen, Haojie
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1470950314, G7532033765
OpenAlex ID: W7224954251