Balanced code[1]

Description

An even-length-\(n\) binary or \(q\)-ary code whose codewords all have a Hamming weight of \(n/2\).

Protection

Can detect unidirectional errors, such as a zero going to a one.

Encoding

Efficient encoder [1].

Decoding

Efficient decoder [1][2][3].

Realizations

Balanced length-eight code, known as a 6b/8b encoding, used for balancing direct current in a communications system [4]

Parent

Child

  • Hadamard code — Each Hadamard codeword has length \(2^m\) and Hamming weight of \(2^{m-1}\), making this code balanced.

References

[1]
D. Knuth, “Efficient balanced codes”, IEEE Transactions on Information Theory 32, 51 (1986). DOI
[2]
S. Al-Bassam and B. Bose, “On balanced codes”, IEEE Transactions on Information Theory 36, 406 (1990). DOI
[3]
K. A. Schouhamer Immink and J. H. Weber, “Very Efficient Balanced Codes”, IEEE Journal on Selected Areas in Communications 28, 188 (2010). DOI
[4]
K. A. S. Immink. Codes for mass data storage systems. Shannon Foundation Publisher, 2004.

Zoo code information

Internal code ID: balanced

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Zoo Code ID: balanced

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/properties/weight/balanced.yml.