Linear codes from projective spaces
Michel Lavrauw, Leo Storme, Geertrui Van de Voorde · Contemporary mathematics - American Mathematical Society · 2010
The linear code $\\C_{s,t}(n,q)$ of $s$-spaces and $t$-spaces in a projective space $\\PG(n,q)$, $q=p^h$, $p$ prime, is defined as the vector space spanned over $\\mathbb{F}_p$ by the rows of the incidence matrix of $s$-spaces and $t$-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970's. In this paper, we give an overview of what is currently known about these codes and their duals.