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\(q\)-ary linear code over \(\mathbb{Z}_q\)

Description

A linear code encoding \(K\) states (codewords) in \(n\) coordinates over the ring \(\mathbb{Z}_q\) of integers modulo \(q\).

Cousin

  • Modular-qudit CSS code— The modular-qudit CSS construction uses two related \(q\)-ary linear codes over \(\mathbb{Z}_q\), \(C_X\) and \(C_Z\).

Member of code lists

Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(q\)-ary code over \(\mathbb{Z}_q\)
Parents
\(q\)-ary code over \(\mathbb{Z}_q\)
\(R\)-linear codeECC
\(q\)-ary linear code over \(\mathbb{Z}_q\)
Children
Quaternary linear code over \(\mathbb{Z}_4\)
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Zoo Code ID: q-ary_linear_over_zq

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

Cite as:

“\(q\)-ary linear code over \(\mathbb{Z}_q\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_linear_over_zq

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/over_zq/q-ary_linear_over_zq.yml.