Description
A block code of length \(n\) over an alphabet is reversible if, for each codeword \(c_1 c_2 \cdots c_n\), the reversed string \(c_n \cdots c_2 c_1\) is also a codeword.Notes
Reversible cyclic codes are studied in [1; Sec. 2.10].Cousins
- Cyclic linear \(q\)-ary code— A reversible cyclic code is a cyclic code with self-reciprocal generator polynomial and is an LCD code [1; Thm. 2.10.3].
- Linear code with complementary dual (LCD)— A reversible cyclic code is a cyclic code with self-reciprocal generator polynomial and is an LCD code [1; Thm. 2.10.3].
- Quantum tensor-product code— Reversible cyclic codes can be used to construct quantum tensor-product codes [2].
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Reversible code
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References
- [1]
- C. Ding, “Cyclic Codes over Finite Fields.” Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
- [2]
- J. Fan, Y. Li, M.-H. Hsieh, and H. Chen, “On Quantum Tensor Product Codes”, (2017) arXiv:1605.09598
Page edit log
- Victor V. Albert (2022-01-02) — most recent
Cite as:
“Reversible code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/reversible