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.
@article{arxiv.1909.00207,
title = {On planes through points off the twisted cubic in $\mathrm{PG}(3,q)$ and multiple covering codes},
author = {Daniele Bartoli and Alexander A. Davydov and Stefano Marcugini and Fernanda Pambianco},
journal= {arXiv preprint arXiv:1909.00207},
year = {2020}
}
Comments
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