# Newman-Moore code[1]

## Description

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].

## Protection

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

## Decoding

Efficient decoder [2].

## Parents

## Cousins

- Hamiltonian-based code — Newman-Moore codewords form the ground-state space of a class of exactly solvable spin-glass models with three-body interactions.
- 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.

## References

- [1]
- 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
- [2]
- D. R. Chowdhury et al., “Design of CAECC - cellular automata based error correcting code”, IEEE Transactions on Computers 43, 759 (1994) DOI
- [3]
- 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
- [4]
- T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831

## Page edit log

- Victor V. Albert (2023-04-12) — most recent

## Cite as:

“Newman-Moore code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/newman_moore