Octacode[13] 

Description

The unique self-dual linear code of length 8 and Lee distance 6 over \(\mathbb{Z}_4\) with generator matrix \begin{align} \begin{pmatrix} 3 & 3 & 2 & 3 & 1 & 0 & 0 & 0\\ 3 & 0 & 3 & 2 & 3 & 1 & 0 & 0\\ 3 & 0 & 0 & 3 & 2 & 3 & 1 & 0\\ 3 & 0 & 0 & 0 & 3 & 2 & 3 & 1 \end{pmatrix}\,. \tag*{(1)}\end{align}

Parents

Cousins

References

[1]
J. H. Conway and N. J. A. Sloane, “Self-dual codes over the integers modulo 4”, Journal of Combinatorial Theory, Series A 62, 30 (1993) DOI
[2]
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
[3]
E. M. Rains and N. J. A. Sloane, “Self-Dual Codes”, (2002) arXiv:math/0208001
[4]
Self-Dual Codes and Invariant Theory (Springer-Verlag, 2006) DOI
[5]
A. R. Hammons et al., “The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes”, IEEE Transactions on Information Theory 40, 301 (1994) DOI
[6]
Feng-Wen Sun and H. C. A. van Tilborg, “The Leech lattice, the octacode, and decoding algorithms”, IEEE Transactions on Information Theory 41, 1097 (1995) DOI
[7]
A. Bonnecaze et al., “Niemeier lattices and Type II codes over Z4”, Discrete Mathematics 205, 1 (1999) DOI
[8]
A. Bonnecaze and P. Solé, “Quaternary constructions of formally self-dual binary codes and unimodular lattices”, Algebraic Coding 194 (1994) DOI
[9]
A. Bonnecaze, P. Sole, and A. R. Calderbank, “Quaternary quadratic residue codes and unimodular lattices”, IEEE Transactions on Information Theory 41, 366 (1995) DOI
[10]
Forney Jr GD, Sloane NJ, Trott MD. The Nordstrom-Robinson code is the binary image of the octacode. In Coding and Quantization: DIMACS/IEEE workshop 1992 Oct 19 (pp. 19-26). Amer. Math. Soc..
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Zoo Code ID: octacode

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/octacode.yml.