On planes through points off the twisted cubic in $\mathrm{PG}(3,q)$ and multiple covering codes

Abstract

Let $\mathrm{PG}(3,q)$ be the projective space of dimension three over the finite field with $q$ elements. Consider a twisted cubic in $\mathrm{PG}(3,q)$. The structure of the point-plane incidence matrix in $\mathrm{PG}(3,q)$ with respect to the orbits of points and planes under the action of the stabilizer group of the twisted cubic is described. This information is used to view generalized doubly-extended Reed-Solomon codes of codimension four as asymptotically optimal multiple covering codes.

27 pages, 2 tables, 31 references, the text is edited, Remarks 2.8 and 7.4 are added, Proposition 6.3 and its Proof are given in more detail, the list of references is extended

References in corpus (1)

• On deep holes of generalized Reed-Solomon codes