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
- Self-dual additive code — The dodecacode is trace-Hermitian self-dual additive.
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
Page edit log
- Victor V. Albert (2022-08-11) — most recent
Cite as:
“Dodecacode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dodecacode