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.
Linear codes from projective spaces
LAVRAUW, MICHEL;
2010
Abstract
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.File in questo prodotto:
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