5 problems

Reed–Muller codes have codeword supports that can form combinatorial $t$-designs, where $t$ is the design strength. One-step majority-logic decoding (1S-MLD) uses these designs to…

BEC–BSC twin-Reed–Muller conjecture. The twin-Reed–Muller codes for the BEC and BSC are equivalent; that is, for some $\epsilon=o(1/n)$,

Layer-crossing conjecture.

Twin-Reed–Muller conjecture. The twin-Reed–Muller code is the Reed–Muller code; equivalently, for $i,j\in[n]$,

Reed–Muller capacity conjecture. Reed–Muller codes achieve the capacity of these channels: their communication threshold agrees with $1-p$ for the Binary Erasure Channel and with…