# Lattice-shell code[1]

## Description

Spherical code whose codewords are scaled versions of points on a lattice. Each code is constructed by normalizing a set of lattice vectors in one or more shells, i.e., sets of lattice points lying on a hypersphere.

## Notes

See [2; Ch. 10] for tables of lattice-shell codes.

## Parent

## Children

## Cousins

- Lattice-based code — Lattice-shell codes consists of lattice points that have been normalized.
- Cyclic code — Lattice-shell codewords are often permutations of a particular set of reference vectors, meaning that a cyclic permutation of a codeword yields another codeword.

## References

- [1]
- N. Sloane, “Tables of sphere packings and spherical codes”, IEEE Transactions on Information Theory 27, 327 (1981) DOI
- [2]
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.

## Page edit log

- Victor V. Albert (2022-11-16) — most recent

## Cite as:

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