Catching three cheaters with a tesseract: Reed–Muller codes on the hypercube (part 2)

Thu, 08 Oct 2026 00:00:00 +0000

A reconstruction. The original sequel to part 1 (April 1, 2013, first published as “Just another generalized version of Hamming Code – Hypercube representation”) was lost. This version rebuilds it from that post and from the ECC-HyperCube code that followed it (first commit August 29, 2013, kept unchanged as the record of the original). The ideas are the 2013 ones; the wording and examples are new.

Same tesseract, one level deeper

Part 1 ended with a problem. On the cube, two cheaters made the faces point at an innocent seat, and the magician blamed number 4. The tesseract version, Hamming (15, 11), has the same weakness: its four groups catch one cheater, never two.

reed-muller on Intuitive Information

Catching three cheaters with a tesseract: Reed–Muller codes on the hypercube (part 2)

Same tesseract, one level deeper