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Bounded-energy code

Alternative Names: Spherical cluster.

Description

Code whose codewords are points lying on or inside a real or complex ball; the squared radius is called the energy.

Member of code lists

Primary Hierarchy

Classical Domain
Analog Kingdom
Analog codeECC
Parents
Analog code
Bounded-energy codes are analog codes constrained to lie on or inside a sphere.
Bounded-energy code
Children
Simplex integer-based code
Points of a discrete simplex \(\Delta_{q,N}\) lie in a \(q\)-ball of radius \(N\).
Modulation scheme
Constant-energy spherical codePolytope Polyhedron Lattice-shell Spherical design
Constant-energy codes are bounded-energy codes constrained to lie on a sphere.
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Zoo Code ID: points_into_balls

Cite as:
“Bounded-energy code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/points_into_balls, arXiv:2606.11484
BibTeX:
@incollection{eczoo_points_into_balls,
title={Bounded-energy 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/points_into_balls}
}
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Permanent link:
https://errorcorrectionzoo.org/c/points_into_balls

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/analog/points_into_balls.yml.