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\(q\)-ary repetition code

Description

An \([n,1,n]_q\) code encoding consisting of codewords \((j,j,\cdots,j)\) for \(j \in GF(q)\). 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.

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 \(t\)-design Universally optimal ECC
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.