\(q\)-ary repetition code 

Description

An \([n,1,n]_q\) code encoding consisting of codewords \((j,j,\cdots,j)\) for \(j \in GF(q)\). The length \(n\) needs to be an odd number, since the receiver will pick the majority to recover the information.

Protection

Detects errors on up to \(\frac{n-1}{2}\) coordinates, corrects erasure errors on up to \(\frac{n-1}{2}\) coordinates.

Parents

Cousins

References

[1]
P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[2]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
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Zoo Code ID: q-ary_repetition

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/easy/q-ary_repetition.yml.