Lattice-based code

Description

Encodes states (codewords) in coordinates of a lattice in the \(n\)-dimensional real coordinate space \(\mathbb{R}^n\). The number of codewords may be infinite because the coordinate space is infinite-dimensional, so various restricted versions have to be constructed in practice. Since lattices are closed under addition, lattice-based codes can be thought of as linear codes over the reals.

Parent

  • Error-correcting code (ECC) — Error-correcting codes are defined for a finite alphabet, so only finite lattice-based codes are children.

Cousins

  • Linear binary code — Since lattices are closed under addition, lattice-based codes can be thought of as linear codes over the reals.
  • Group-based code — Group-based codes whose alphabet is based on the group \(\mathbb{R}\) are lattice-based codes.
  • Multi-mode GKP code — Multimode GKP codes are quantum analogues of lattice-based codes.

Zoo code information

Internal code ID: points_into_lattices

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: points_into_lattices

Cite as:
“Lattice-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/points_into_lattices
BibTeX:
@incollection{eczoo_points_into_lattices, title={Lattice-based code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/points_into_lattices} }
Permanent link:
https://errorcorrectionzoo.org/c/points_into_lattices

Cite as:

“Lattice-based code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/points_into_lattices

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/lattices/points_into_lattices.yml.