Description
A \(q\)-ary code whose codewords are closed under addition, i.e., for any codewords \(x,y\), \(x+y\) is also a codeword.
Parents
- \(q\)-ary code
- Linear code over \(G\) — Additive \(q\)-ary codes are linear over \(G=GF(q)\) since Galois fields are Abelian groups under addition.
Children
- Twisted BCH code
- 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 — Galois-qudit stabilizer codes are the closest quantum analogues of additive codes 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)
Cite as:
“Additive \(q\)-ary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_additive