On planes through points off the twisted cubic in PG(3, q) and multiple covering codes

摘要

Let PG(3, q) be the projective space of dimension three over the finite field with q elements. Consider a twisted cubic in PG(3, q). The structure of the point-plane incidence matrix in 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. (C) 2020 Elsevier Inc. All rights reserved.