Constant-weight code 


A block code over a field or a ring whose codewords all have the same Hamming weight \(w\). The complement of a binary constant-weight code is a constant-weight code obtained by interchanging zeroes and ones in the codewords. The set of all binary codewords of length \(n\) forms the Johnson space \(J(n,w)\) [14].

Constant-weight codes that contain all strings of some fixed Hamming weight are known as \(m\)-in-\(n\) or \({n \choose m}\) codes.


See Ref. [5] for upper bounds on \(K\) for \((n,K,d)_q\) constant-weight binary codes.


Radio-network frequency hopping [6].


Tables of binary constant-weight codes for \(n \leq 28\) [7] and \(n > 28\) [6]. Other code constructions also exist for codes over fields [8] or rings [9].See book [10] for (Johnson) bounds on the size of constant-weight codes.





Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973): vi+-97.
P. Delsarte, “Association schemes and t-designs in regular semilattices”, Journal of Combinatorial Theory, Series A 20, 230 (1976) DOI
Ph. Delsarte, “Hahn Polynomials, Discrete Harmonics, andt-Designs”, SIAM Journal on Applied Mathematics 34, 157 (1978) DOI
V. I. Levenshtein, “Designs as maximum codes in polynomial metric spaces”, Acta Applicandae Mathematicae 29, 1 (1992) DOI
K. Zeger, A. Vardy, and E. Agrell, “Upper bounds for constant-weight codes”, IEEE Transactions on Information Theory 46, 2373 (2000) DOI
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
A. E. Brouwer et al., “A new table of constant weight codes”, IEEE Transactions on Information Theory 36, 1334 (1990) DOI
Fang-Wei Fu, A. J. Han Vinck, and Shi-Yi Shen, “On the constructions of constant-weight codes”, IEEE Transactions on Information Theory 44, 328 (1998) DOI
T. Etzion, “Optimal constant weight codes over Zk and generalized designs”, Discrete Mathematics 169, 55 (1997) DOI
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
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Zoo Code ID: constant_weight

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“Constant-weight code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_constant_weight, title={Constant-weight code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Constant-weight code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.