Description
Evaluation code of polynomials evaluated on points lying on a Grassmannian \({\mathbb{G}}(\ell,m)\).
Parent
- Flag-variety code — Grassmannian codes are flag-variety evaluation codes with the flag variety being a Grassmannian.
Cousins
- Griesmer code — The binary Grassmannian \([35,6,16]\) code, whose points lie on the Grassmannian \({\mathbb{G}(2,4)}\), attains the Griesmer bound [4].
- Schubert code — Schubert varieties are subvarieties of Grassmannians, and Schubert codes were initially constructed as a generalization of Grassmannian codes.
References
- [1]
- C. T. Ryan, An application of Grassmannian varieties to coding theory. Congr. Numer. 57 (1987) 257–271.
- [2]
- C.T. Ryan, Projective codes based on Grassmann varieties, Congr. Numer. 57, 273–279 (1987).
- [3]
- C. T. Ryan and K. M. Ryan, “The minimum weight of the Grassmann codes C(k,n),”, Discrete Applied Mathematics 28, 149 (1990) DOI
- [4]
- J. B. Little, “Algebraic geometry codes from higher dimensional varieties”, (2008) arXiv:0802.2349
Page edit log
- Victor V. Albert (2022-08-10) — most recent
Cite as:
“Grassmannian code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/grassmannian