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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.

Cousins

Member of code lists

Primary Hierarchy

Parents
Additive \(q\)-ary codes are linear over \(G=GF(q)\) since Galois fields are Abelian groups under addition.
Additive \(q\)-ary code
Children
For \(q>2\), additive codes need not be linear since linearity also requires closure under multiplication.

References

[1]
M. Ran and J. Snyders, “On cyclic reversible self-dual additive codes with odd length over Z/sub 2//sup 2/”, IEEE Transactions on Information Theory 46, 1056 (2000) DOI
[2]
R. Li, Y. Ren, C. Guan, and Y. Liu, “Geometry of symplectic group and optimal EAQECC codes”, (2025) arXiv:2501.15465
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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/edit/main/codes/classical/q-ary_digits/additive/q-ary_additive.yml.