Additive \(q\)-ary code
Description
A \(q\)-ary code whose codewords are closed under addition, i.e., for any codewords \(x,y\), \(x+y\) is also a codeword.
Parent
Children
- Dual additive code
- Linear \(q\)-ary code — For \(q>2\), additive codes need not be linear since linearity also requires closure under multiplication.
Cousin
- 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)
Zoo code information
Cite as:
“Additive \(q\)-ary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_additive