Cyclic code
Description
A code \(C\) of length \(n\) over an alphabet is cyclic if, for each string \(c_1 c_2 \cdots c_n\in C\), the cyclically shifted string \(c_n c_1 \cdots c_{n-1}\in C\).
Parent
Children
Cousins
- Bose–Chaudhuri–Hocquenghem (BCH) code
- Galois-qudit polynomial code (QPyC)
- Majorana stabilizer code — Cyclic codes can be used to construct translation-invariant Majorana stabilizer codes, provided that they are also weakly self-dual [1].
- Prime-qudit polynomial code (QPyC)
- Quantum cyclic code
- Reed-Solomon (RS) code — If the length divides \(q-1\), then it is possible to construct a cyclic RS code.
- \(q\)-ary group code — A length-\(n\) cyclic code is an abelian group code for the cyclic group with \(n\) elements \( \mathbb{Z}_n \).
Zoo code information
References
- [1]
- Sagar Vijay and Liang Fu, “Quantum Error Correction for Complex and Majorana Fermion Qubits”. 1703.00459
Cite as:
“Cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cyclic