Author

Freeman Slaughter

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Preprint Oct 2026

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 $\rho(r,n)$ denote its covering radius. It is known that $242\le\rho(1,9)\le 244$, and the determination of $\rho(1,9)$ is a long-standing open question. We give a computer-assisted proof that $\rho(1,9)=242$, leveraging the classificatio...

Xiang-Dong Hou, Evelyn Sabo, Freeman Slaughter · 1 citation

Preprint Oct 2026

A Bounded-Defect Construction for the Mondrian Art Problem

We construct an infinite family of solutions to the Mondrian art problem with absolute defect bounded above by $280$, of side lengths $n_0 = 315$, $n_1 = 106785$, and $n_{j+2} = 340n_{j+1} - n_j$, where $n_j$ is congruent to $315 \pmod{630}$. This absolute bound shows that the minimum defect does not necessarily increa...

Cooper O'Kuhn, Freeman Slaughter · 0 citations