PreprintarXiv licencearXiv
On the MDS conjecture in even characteristic
Abstract
We prove that every nontrivial linear [n,k] maximum distance separable (MDS) code over a finite field Fq of characteristic two satisfies n≤ q+1, except in dimensions k=3 and k=q−1, where n≤ q+2. This resolves the linear MDS conjecture in even characteristic.
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BibTeX
@misc{chen2026conjecture,
title = {{On the MDS conjecture in even characteristic}},
author = {Bocong Chen and Jing Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28208},
eprint = {2610.28208},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28208},
}
RIS
TY - UNPB
TI - On the MDS conjecture in even characteristic
AU - Bocong Chen
AU - Jing Huang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28208
UR - https://arxiv.org/abs/2610.28208
AB - We prove that every nontrivial linear [n,k] maximum distance separable (MDS) code over a finite field F_q of characteristic two satisfies n≤ q+1, except in dimensions k=3 and k=q−1, where n≤ q+2. This resolves the linear MDS conjecture in even characteristic.
ER -