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].
Parents
- \(q\)-ary simplex code — The tetracode is equivalent to \(S(3,2)\).
- \(q\)-ary Hamming code — The tetracode is equivalent to the \(r=2\) \(3\)-ary Hamming code.
- Self-dual linear code — The tetracode is Euclidean self-dual.
- Maximum distance separable (MDS) code
- Extended GRS code — The tetracode is an extended RS code [1; pg. 81]
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
Page edit log
- Victor V. Albert (2022-08-09) — most recent
Cite as:
“Tetracode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tetracode