Construction-\(A\) code[1]
Description
Sphere packing constructed from a binary \((n,K)\) code using Construction \(A\) [2]. Each binary codeword \(c\) of the code is mapped to an infinite set of points \(x\) such that \(x = c\) modulo two. If the underlying binary code is linear, then the resulting set of points forms a lattice.
Parent
Children
Cousins
- Binary code — Each binary code yields a sphere packing under Construction \(A\).
- Linear binary code — Every binary linear code yields a lattice code under Construction \(A\).
- Best \((10,40,4)\) code — Using Construction \(A\), the Best code yields \(P_{10c}\), a non-lattice sphere packing in 10 dimensions that is the densest known [3][2; pg. 140].
- Julin-Golay code — Using Construction \(A\), the Julin-Golay codes yield non-lattice sphere-packings that hold records in 9 and 11 dimensions.
References
- [1]
- J. Leech, “Notes on Sphere Packings”, Canadian Journal of Mathematics 19, 251 (1967) DOI
- [2]
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
- [3]
- J. Leech and N. J. A. Sloane, “Sphere Packings and Error-Correcting Codes”, Canadian Journal of Mathematics 23, 718 (1971) DOI
Page edit log
- Victor V. Albert (2022-11-08) — most recent
Cite as:
“Construction-\(A\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/construction_a