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\(q\)-ary repetition code

Description

An \([n,1,n]_q\) code encoding consisting of codewords \((j,j,\cdots,j)\) for \(j \in \mathbb{F}_q\). 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.

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Quasi group-algebra code
Group-algebra codeECC
Cyclic linear \(q\)-ary codeCyclic Constacyclic Skew-cyclic ECC
Parents
Cyclic linear \(q\)-ary code
The \(q\)-ary repetition code is cyclic with generator polynomial \(1+x+\cdots+x^{n-1}\).
\(q\)-ary sharp configurationOA Sharp configuration Universally optimal ECC \(t\)-design
The \(q\)-ary repetition code is a \(q\)-ary sharp configuration [2; Table 12.1].
\(q\)-ary repetition code

References

[1]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
[2]
P. Boyvalenkov, D. Danev, “Linear programming bounds.” Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
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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.