Cyclic code[15] 

Description

A code of length \(n\) over an alphabet is cyclic if, for each codeword \(c_1 c_2 \cdots c_n\), the cyclically shifted string \(c_n c_1 \cdots c_{n-1}\) is also a codeword.

Parent

Children

Cousins

  • Lattice-shell code — Lattice-shell codewords are often permutations of a particular set of reference vectors, meaning that a cyclic permutation of a codeword yields another codeword.
  • Cyclic quantum code

References

[1]
E. Prange, Cyclic Error-Correcting Codes in Two Symbols, TN-57-/03, (September 1957)
[2]
E. Prange, Some cyclic error-correcting codes with simple decoding algorithms, TN-58-156, (April 1958)
[3]
E. Prange, The use of coset equivalence in the analysis and decoding of group codes, TN-59-/64, (1959)
[4]
E. Prange, An algorithm for factoring xn - I over a finite field. TN-59-/75, (October 1959)
[5]
W. W. Peterson and E. J. Weldon, Error-correcting codes. MIT press 1972.
[6]
Self-Dual Codes and Invariant Theory (Springer-Verlag, 2006) DOI
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Zoo Code ID: cyclic

Cite as:
“Cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cyclic
BibTeX:
@incollection{eczoo_cyclic,
  title={Cyclic code},
  booktitle={The Error Correction Zoo},
  year={2022},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/cyclic}
}
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Permanent link:
https://errorcorrectionzoo.org/c/cyclic

Cite as:

“Cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cyclic

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/properties/block/cyclic/cyclic.yml.