Dodecacode[1,2] 

Description

The unique trace-Hermitian self-dual additive \((12,4^6,6)_4\) code. Its codewords are cyclic permutations of \((\omega 10100100101)\), where \(GF(4)=\{0,1,\omega,\bar{\omega}\}\) [3; Sec. 2.4.8]. Another generator matrix can be found in [4; Ex. 9.10.8].

The dodecacode is a self-dual additive code, and there is no self-dual linear code with the same parameters [5].'

Parent

References

[1]
A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006
[2]
G. Hoehn, “Self-dual Codes over the Kleinian Four Group”, (2000) arXiv:math/0005266
[3]
Self-Dual Codes and Invariant Theory (Springer-Verlag, 2006) DOI
[4]
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, 2003) DOI
[5]
C. W. H. Lam and V. Pless, “There is no (24, 12, 10) self-dual quaternary code”, IEEE Transactions on Information Theory 36, 1153 (1990) DOI
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Zoo Code ID: dodecacode

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/easy/dodecacode.yml.