Covering radius of RM(1,m) for odd m greater than 9

Determine the covering radius of RM(1,m) for every odd integer m greater than 9, for which the covering-radius problem remains completely open.

Background

After discussing the resolved case m=9, the paper states that the covering radius of the first-order Reed–Muller code remains unresolved for all larger odd numbers of variables. The statement concerns the general family RM(1,m), not the RM(1,9) instance settled by the paper.

References

For odd $m > 9$, the covering radius of RM(1,$m$) is completely open.

— The Covering Radius of the Reed--Muller Code RM(1,9) is 242  (2610.17871 - Wang et al., 13 Oct 2026) in Section 1, Introduction