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

Alternative names: Group code over \(\mathbb{Z}_q\).

Description

A code encoding \(K\) states (codewords) in \(n\) coordinates over the ring \(\mathbb{Z}_q\) of integers modulo \(q\) that is closed under codeword addition.

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Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(q\)-ary code over \(\mathbb{Z}_q\)
Parents
\(q\)-ary code over \(\mathbb{Z}_q\)
\(q\)-ary additive code over \(\mathbb{Z}_q\)
Children
\(q\)-ary linear code over \(\mathbb{Z}_q\)Gray
For \(q>2\), additive codes need not be linear since linearity also requires closure under multiplication.
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Zoo Code ID: q-ary_additive_over_zq

Cite as:
“\(q\)-ary additive code over \(\mathbb{Z}_q\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/q-ary_additive_over_zq
BibTeX:
@incollection{eczoo_q-ary_additive_over_zq, title={\(q\)-ary additive code over \(\mathbb{Z}_q\)}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/q-ary_additive_over_zq} }
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Permanent link:
https://errorcorrectionzoo.org/c/q-ary_additive_over_zq

Cite as:

“\(q\)-ary additive code over \(\mathbb{Z}_q\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/q-ary_additive_over_zq

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