Here is a list of codes whose codewords have constant weight.
| Code | Description |
|---|---|
| Combinatorial design | A constant-weight binary code that is mapped into a combinatorial \(t\)-design. |
| Constant-weight code | A binary code whose codewords all have the same Hamming weight \(w\). |
| One-hot code | A length-\(n\) binary code whose codewords are those with Hamming weight one. The reverse of this code, where all codewords have Hamming weight \(n-1\) is called a one-cold code. |
| One-versus-one (OVO) code | A length-\(n\) ternary code over \(\{\pm 1,0\}\) whose whose generator matrix has columns with one \(+1\), one \(-1\), and with the rest of the entries zero. |
| Weight-two code | A length-\(n\) binary code whose codewords all have Hamming weight two. Such codes provide slightly extra redundancy for storage of small-scale information such as ZIP codes or decimal digits. |
| \([2^m-1,m,2^{m-1}]\) simplex code | A member of the equidistant code family that is dual to the \([2^m,2^m-m-1,3]\) Hamming family. The columns of its generator matrix are in one-to-one correspondence with the elements of the projective space \(PG(m-1,2)\), with each column being a chosen representative of the corresponding element. The codewords form a \((2^m,2^m+1)\) simplex spherical code under the antipodal mapping. |
| \([7,3,4]\) simplex code | Second-smallest member of the simplex code family. The columns of its generator matrix are in one-to-one correspondence with the elements of the projective space \(PG(2,2)\), with each column being a chosen representative of the corresponding element. The codewords form a \((8,9)\) simplex spherical code under the antipodal mapping. |
