Newman-Moore code[1] 


Member of a family of \([L^2,O(L),O(L^{\frac{\log 3}{\log 2}})]\) binary linear codes on \(L\times L\) square lattices that form the ground-state subspace of a class of exactly solvable spin-glass models with three-body interactions. The codewords resemble the Sierpinski triangle on a square lattice, which can be generated by a cellular automaton [2].


Code parameters nearly saturate the classical version of the BPT bound, based on numerical simulations and analytical arguments [3; Appx. A].


Efficient decoder [2].



  • X-cube model code — Generalized X-cube models [4] are constructed from a product of the repetion (1D Ising) code and the Newman-Moore code.


M. E. J. Newman and C. Moore, “Glassy dynamics and aging in an exactly solvable spin model”, Physical Review E 60, 5068 (1999) arXiv:cond-mat/9707273 DOI
D. R. Chowdhury et al., “Design of CAECC - cellular automata based error correcting code”, IEEE Transactions on Computers 43, 759 (1994) DOI
S. Bravyi, D. Poulin, and B. Terhal, “Tradeoffs for Reliable Quantum Information Storage in 2D Systems”, Physical Review Letters 104, (2010) arXiv:0909.5200 DOI
T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831
Page edit log

Your contribution is welcome!

on (edit & pull request)— see instructions

edit on this site

Zoo Code ID: newman_moore

Cite as:
“Newman-Moore code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_newman_moore, title={Newman-Moore code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:

Cite as:

“Newman-Moore code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.