PreprintCC BY 4.0arXiv
The covering radius of RM(1,9) is precisely 242
Abstract
Let RM(r,n) be the rth order Reed-Mullet code of length 2n, and let ρ(r,n) denote its covering radius. It is known that 242≤ρ(1,9)≤ 244, and the determination of ρ(1,9) is a long-standing open question. We give a computer-assisted proof that ρ(1,9)=242, leveraging the classification of the $349$ orbits in RM(3,9)/RM(2,9) under GL(9,2) [1,3]. The notebook to verify the computer search portion, Verify_RM(1,9).ipynb, contains all data and recomputes each check, and may be found in the repository https://github.com/FreemanSlaughter/Covering-Radius.
Related
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BibTeX
@misc{hou2026covering,
title = {{The covering radius of RM(1,9) is precisely 242}},
author = {Xiang-Dong Hou and Evelyn Sabo and Freeman Slaughter},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00070},
eprint = {2611.00070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The covering radius of RM(1,9) is precisely 242
AU - Xiang-Dong Hou
AU - Evelyn Sabo
AU - Freeman Slaughter
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00070
UR - https://arxiv.org/abs/2611.00070
AB - Let RM(r,n) be the rth order Reed-Mullet code of length 2^n, and let ρ(r,n) denote its covering radius. It is known that 242≤ρ(1,9)≤ 244, and the determination of ρ(1,9) is a long-standing open question. We give a computer-assisted proof that ρ(1,9)=242, leveraging the classification of the $349$ orbits in RM(3,9)/RM(2,9) under GL(9,2) [1,3]. The notebook to verify the computer search portion, Verify_RM(1,9).ipynb, contains all data and recomputes each check, and may be found in the repository https://github.com/FreemanSlaughter/Covering-Radius.
ER -