Description
Extension of the \([7,4,3]\) Hamming code by a parity-check bit. The smallest doubly-even self-dual code.
Parent
Cousins
- Divisible code — The extended Hamming code code is the smallest double-even self-dual code.
- \(E_8\) Gosset lattice code — The \([8,4,4]\) extended Hamming code yields the \(E_8\) Gosset lattice code via the mod-two lattice construction [4; Ex. 10.5.2].
- \([7,4,3]\) Hamming code — The Hamming code can be extended by a parity-check bit to yield the \([8,4,4]\) extended Hamming code, the smallest doubly-even self-dual code.
- Octacode — The octacode reduces modulo-two to the \([8,4,4]\) extended Hamming code [5].
References
- [1]
- C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 379 (1948) DOI
- [2]
- R. W. Hamming, “Error Detecting and Error Correcting Codes”, Bell System Technical Journal 29, 147 (1950) DOI
- [3]
- M. J. E. Golay, Notes on digital coding, Proc. IEEE, 37 (1949) 657.
- [4]
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
- [5]
- Self-Dual Codes and Invariant Theory (Springer-Verlag, 2006) DOI
Page edit log
- Victor V. Albert (2022-12-21) — most recent
Cite as:
“\([8,4,4]\) extended Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/hamming844