PreprintCC0arXiv
MDS Algebraic Geometry Codes of Square-Root Length on Hyperelliptic Curves
Abstract
For every fixed genus g≥2 and every 0<ρ<1, we construct maximum distance separable (MDS) algebraic geometry codes over Fq for all sufficiently large odd squares q. Their parameters are [n,⌊ρn⌋,n−⌊ρn⌋+1]q with n=√q+1+Og(q1/4). The codes use full Riemann--Roch spaces on genus-g hyperelliptic curves. They are not monomially equivalent to generalized Reed--Solomon (GRS) codes when q is sufficiently large. An infinite subfamily has exact length n=√q+2gq1/4+1.
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BibTeX
@misc{hu2026algebraic,
title = {{MDS Algebraic Geometry Codes of Square-Root Length on Hyperelliptic Curves}},
author = {Chuangqiang Hu and Guorui Ma},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01546},
eprint = {2611.01546},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01546},
note = {CC0},
}
RIS
TY - UNPB
TI - MDS Algebraic Geometry Codes of Square-Root Length on Hyperelliptic Curves
AU - Chuangqiang Hu
AU - Guorui Ma
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01546
UR - https://arxiv.org/abs/2611.01546
AB - For every fixed genus g≥2 and every 0<ρ<1, we construct maximum distance separable (MDS) algebraic geometry codes over F_q for all sufficiently large odd squares q. Their parameters are [n,⌊ρn⌋,n−⌊ρn⌋+1]_q with n=√q+1+O_g(q^1/4). The codes use full Riemann--Roch spaces on genus-g hyperelliptic curves. They are not monomially equivalent to generalized Reed--Solomon (GRS) codes when q is sufficiently large. An infinite subfamily has exact length n=√q+2gq^1/4+1.
ER -