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.

Catching a cheater with a cube: Hamming codes on the hypercube (part 1)

Mon, 01 Apr 2013 00:00:00 +0000

Revised in 2026: the figures are redrawn to match part 2, and the unfinished ending is completed. The rest is the April 2013 post (first published as “Just another generalized version of Hamming Code – Hypercube representation”), lightly edited.

hypercube on Intuitive Information

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

Same tesseract, one level deeper

Catching a cheater with a cube: Hamming codes on the hypercube (part 1)