Tetracode[1] 

Description

The \([4,2,3]_3\) self-dual MDS code with generator matrix \begin{align} \begin{pmatrix}1 & 0 & 1 & 1\\ 0 & 1 & 1 & 2 \end{pmatrix}~, \tag*{(1)}\end{align} where \(GF(3) = \{0,1,2\}\). Has connections to lattices [1].

Notes

See corresponding MinT database entry [2].

Parents

Cousin

  • Ternary Golay code — Extended ternary Golay codewords can be obtained from tetracodewords [1]. The tetracode can be used to decode the extended ternary Golay code [3].

References

[1]
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
[2]
Rudolf Schürer and Wolfgang Ch. Schmid. “Tetracode.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_CTetra.html
[3]
V. Pless, “Decoding the Golay codes”, IEEE Transactions on Information Theory 32, 561 (1986) DOI
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Zoo Code ID: tetracode

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

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

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