Classical fractal liquid code

Classical fractal liquid code[1,2]

Description

Member of a family of \([L^D,O(L^{D-1}),O(L^{D-\epsilon})]_p\) linear codes on \(D\)-dimensional square lattices of side length \(L\) and for some prime \(p\) and \(\epsilon > 0\) that is based on \(p\)-ary generalizations of the Sierpinski triangle.

Protection

Parameters of some code families saturate the classical version of the BPT bound [1].

Cousin

Commuting-projector Hamiltonian code— Classical fractal liquid codewords form the ground-state space of a class of exactly solvable spin-glass Ising models with three-body interactions.

Member of code lists

Primary Hierarchy

Classical Domain

Galois-field Kingdom

\(q\)-ary codeECC

Additive \(q\)-ary codeECC

Linear \(q\)-ary codeECC

Parents

Linear \(q\)-ary code

Linear code over \(\mathbb{Z}_q\)ECC

Quantum-inspired classical block codeECC

Classical fractal liquid code

Children

Newman-Moore code

References

[1]: B. Yoshida, “Information storage capacity of discrete spin systems”, Annals of Physics 338, 134 (2013) arXiv:1111.3275 DOI
[2]: B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI

Page edit log

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

Cite as:

“Classical fractal liquid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/classical_fractal_liquid

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml.