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Unitary code[1,2]

Description

Encodes \(K\) states (codewords) into the unitary group \(U(N)\).

Protection

LP bounds on the unitary group have been established [2,3].

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Group Kingdom
Group-alphabet codeECC
Parents
Group-alphabet code
Homogeneous-space codeECC
The unitary group is a compact symmetric space \(G/H\) with \(G=U(N)\times U(N)\) and \(H = U(N)\) [4; Table 3].
Unitary code
Children
Unitary \(t\)-design
Unitary \(t\)-designs are designs on the unitary group \(U(N)\).
Alamouti code
Codewords of the Alamouti code are two-dimensional unitary matrices.

References

[1]
A. Roy, “Bounds for codes and designs in complex subspaces”, (2008) arXiv:0806.2317
[2]
A. Roy and A. J. Scott, “Unitary designs and codes”, Designs, Codes and Cryptography 53, 13 (2009) arXiv:0809.3813 DOI
[3]
J. Creignou and H. Diet, “Linear programming bounds for unitary space time codes”, (2008) arXiv:0803.1227
[4]
C. Bachoc, D. C. Gijswijt, A. Schrijver, and F. Vallentin, “Invariant Semidefinite Programs”, International Series in Operations Research & Management Science 219 (2011) arXiv:1007.2905 DOI
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Zoo Code ID: unitary

Cite as:
“Unitary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/unitary
BibTeX:
@incollection{eczoo_unitary, title={Unitary code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/unitary} }
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Cite as:

“Unitary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/unitary

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/groups/unitary/unitary.yml.