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Berman code[1–3]

Description

A member of a family of codes that is recursively constructed from the single parity-check code via a construction that is similar to the \((u|u+v)\) construction [3]. Berman codes include RM codes as a special case.

Rate

Achieve capacity of the BEC and BMS channels [3].

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Parents
Linear binary code
Berman code
Children
Reed-Muller (RM) code
Berman codes include RM codes as a special case [3].

References

[1]
S. D. Berman, “Semisimple cyclic and Abelian codes. II”, Cybernetics 3, 17 (1970) DOI
[2]
T. Blackmore and G. H. Norton, “On a family of Abelian codes and their state complexities”, IEEE Transactions on Information Theory 47, 355 (2001) DOI
[3]
L. P. Natarajan and P. Krishnan, “Berman Codes: A Generalization of Reed-Muller Codes that Achieve BEC Capacity”, (2023) arXiv:2202.09981
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Zoo Code ID: berman

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/reed_muller/berman.yml.