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arXiv · 1909.00207

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

Daniele Bartoli·Alexander A. Davydov·Stefano Marcugini·Fernanda Pambianco
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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.

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Daniele Bartoli, Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco. 2019-08-31. On planes through points off the twisted cubic in $\mathrm{PG}(3,q)$ and multiple covering codes. https://arxiv.org/abs/1909.00207

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