Description
\([n,1,n]_q\) binary linear 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
- Cyclic linear \(q\)-ary code — The \(q\)-ary repetition code is cyclic with generator polynomial \(1+x+\cdots+x^{n-1}\).
- \(q\)-ary sharp configuration — The \(q\)-ary repetition code is a \(q\)-ary sharp configuration [1; Table 12.1].
Cousins
- Repetition code
- \(E_6\) root lattice code — The \([3,1,3]_3\) ternary repetition code can be used to obtain the \(E_6\) root lattice code [2; Ex. 10.5.4].
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.
Page edit log
- Victor V. Albert (2022-12-12) — most recent
Cite as:
“\(q\)-ary repetition code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/q-ary_repetition