Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416667 | Linear Algebra and its Applications | 2013 | 14 Pages |
Abstract
The projective space of order n over the finite field Fq, denoted here as Pq(n), is the set of all subspaces of the vector space Fqn. The projective space can be endowed with distance function dS(X,Y)=dim(X)+dim(Y)-2dim(Xâ©Y) which turns Pq(n) into a metric space. With this, an (n,M,d)code Cin projective space is a subset of Pq(n) of size M such that the distance between any two codewords (subspaces) is at least d. Koetter and Kschischang recently showed that codes in projective space are precisely what is needed for error-correction in networks: an (n,M,d) code can correct t packet errors and Ï packet erasures introduced (adversarially) anywhere in the network as long as 2t+2Ï
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michael Braun, Tuvi Etzion, Alexander Vardy,