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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].

The code is not cyclic, but admits a bivariate polynomial representation \(1+x+y\) for its generator matrix.

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].

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Parents
Linear binary code
Classical fractal liquid codeQuantum-inspired classical block Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
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, S. Basu, I. S. Gupta, and P. P. Chaudhuri, “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
[5]
Y. Tan, B. Roberts, N. Tantivasadakarn, B. Yoshida, and N. Y. Yao, “Fracton models from product codes”, Physical Review Research 7, (2025) arXiv:2312.08462 DOI
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Zoo Code ID: newman_moore

Cite as:
“Newman-Moore code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/newman_moore, arXiv:2606.11484
BibTeX:
@incollection{eczoo_newman_moore,
title={Newman-Moore code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/newman_moore}
}
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Permanent link:
https://errorcorrectionzoo.org/c/newman_moore

Cite as:

“Newman-Moore code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/newman_moore, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/quantum_inspired/newman_moore.yml.