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.

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  • 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.
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Zoo code information

Internal code ID: q-ary_additive

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Zoo Code ID: q-ary_additive

Cite as:
“Additive \(q\)-ary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_additive
BibTeX:
@incollection{eczoo_q-ary_additive, title={Additive \(q\)-ary code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/q-ary_additive} }
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Permanent link:
https://errorcorrectionzoo.org/c/q-ary_additive

Cite as:

“Additive \(q\)-ary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_additive

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/q-ary_additive.yml.