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.





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