[Jump to code hierarchy]

Tetracode[1]

Description

The \([4,2,3]_3\) self-dual MDS code that has connections to lattices [1].

A generator matrix is \begin{align} \begin{pmatrix}1 & 0 & 1 & 1\\ 0 & 1 & 1 & 2 \end{pmatrix}~, \tag*{(1)}\end{align} where \(GF(3) = \{0,1,2\}\).

Notes

See corresponding MinT database entry [2].

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. https://mint.sbg.ac.at/desc_CTetra.html
[3]
V. Pless, “Decoding the Golay codes”, IEEE Transactions on Information Theory 32, 561 (1986) DOI
[4]
J. Conway and N. Sloane, “Lexicographic codes: Error-correcting codes from game theory”, IEEE Transactions on Information Theory 32, 337 (1986) DOI
Page edit log

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.