Covering radius of higher-order Reed–Muller codes in nine variables

Determine the covering radius of RM(r,9) within RM(r,9) for every integer r greater than or equal to 5, as this quantity remains unknown.

Background

The paper establishes the covering radius of RM(1,9), but notes that the analogous covering-radius problem in the higher-order Reed–Muller-code setting has not been resolved for r greater than or equal to 5. This identifies an unresolved extension beyond the specific RM(1,9) result proved in the paper.

References

For r\ge 5, the covering radius of RM(1, 9) in RM(r, 9) is also still unknown.

— 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