Additive \(q\)-ary code
A \(q\)-ary code whose codewords are closed under addition, i.e., for any codewords \(x,y\), \(x+y\) is also a codeword.
- Galois-field \(q\)-ary code
- Linear code over \(G\) — Additive \(q\)-ary codes are linear over \(G=GF(q)\) since Galois fields are abelian groups under addition.
- Dual additive code
- Linear \(q\)-ary code — For \(q>2\), additive codes need not be linear since linearity also requires closure under multiplication.
- Galois-qudit stabilizer code — A Galois-qudit stabilizer code is the closest quantum analogue of an additive code over \(GF(q)\) because addition in the field corresponds to multiplication of stabilizers in the quantum case.
Page edit log
- Victor V. Albert (2022-05-19) — most recent
- Shuubham Ojha (2022-05-18)
“Additive \(q\)-ary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_additive