Constant-weight code

Description

Also known as an \(m\)-in-\(n\) or \({n \choose m}\) code. A linear binary or \(q\)-ary code whose codewords all have the same Hamming weight.

Realizations

Radio-network frequency hopping [1].

Notes

Tables of binary constant-weight codes for \(n \leq 28\) [2] and \(n > 28\) [1].See book [3] for (Johnson) bounds on the size of constant-weight codes.

Parent

  • Divisible code — Codes whose codewords have a constant weight of \(m\) are automatically \(m\)-divisible.

Children

Cousin

References

[1]
D. H. Smith, L. A. Hughes, and S. Perkins, “A New Table of Constant Weight Codes of Length Greater than 28”, The Electronic Journal of Combinatorics 13, (2006). DOI
[2]
A. E. Brouwer et al., “A new table of constant weight codes”, IEEE Transactions on Information Theory 36, 1334 (1990). DOI
[3]
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.

Zoo code information

Internal code ID: constant_weight

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Zoo Code ID: constant_weight

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

Cite as:

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

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