← 研踪 PaperTrailarXiv:2610.39364 · v1
A Uniform Upper Bound on the Length of MDS Codes from Genus-Two Curves
首次提交 2026-10-29 12:56
版本更新 2026-10-29 12:56
雷达观测 2026-10-30 11:25
摘要
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 $q\geq125$.
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v1 · 2026-10-29 12:56 · 最新观测版本
A Uniform Upper Bound on the Length of MDS Codes from Genus-Two Curves
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 $q\geq125$.
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