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A Uniform Upper Bound on the Length of MDS Codes from Genus-Two Curves
Abstract
We study the maximal length of MDS algebraic geometry codes from genus-two curves over finite fields. Let C L(D,G) be such a code over 𝔽q, with length n and dimension k. Assume that 3≤ k≤ n−3. We prove that n<(2q+10√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(√q) for the maximal length. The explicit bound is strictly smaller than q+1 when q≥125.
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BibTeX
@misc{chen2026uniform,
title = {{A Uniform Upper Bound on the Length of MDS Codes from Genus-Two Curves}},
author = {Haojie Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39364},
eprint = {2610.39364},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39364},
}
RIS
TY - UNPB
TI - A Uniform Upper Bound on the Length of MDS Codes from Genus-Two Curves
AU - Haojie Chen
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39364
UR - https://arxiv.org/abs/2610.39364
AB - We study the maximal length of MDS algebraic geometry codes from genus-two curves over finite fields. Let C_ L(D,G) be such a code over 𝔽_q, with length n and dimension k. Assume that 3≤ k≤ n−3. We prove that n<(2q+10√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(√q) for the maximal length. The explicit bound is strictly smaller than q+1 when q≥125.
ER -