The covering radius of RM(1,9) is precisely 242
Let $\text{RM}(r,n)$ be the $r$th order Reed-Mullet code of length $2^n$, and let $ρ(r,n)$ denote its covering radius. It is known that $242\leρ(1,9)\le 244$, 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 $\text{RM}(3,9)/\text{RM}(2,9)$ under $\text{GL}(9,2)$ [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.
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