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.
On planes through points off the twisted cubic in PG(3,q) and multiple covering codes
Bartoli D.;Marcugini S.;Pambianco F.
2020
Abstract
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.File in questo prodotto:
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