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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 10/2021

27-08-2021

Twisted cubic and point-line incidence matrix in \(\mathrm {PG}(3,q)\)

Authors: Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco

Published in: Designs, Codes and Cryptography | Issue 10/2021

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Abstract

We consider the structure of the point-line incidence matrix of the projective space \(\mathrm {PG}(3,q)\) connected with orbits of points and lines under the stabilizer group of the twisted cubic. Structures of submatrices with incidences between a union of line orbits and an orbit of points are investigated. For the unions consisting of two or three line orbits, the original submatrices are split into new ones, in which the incidences are also considered. For each submatrix (apart from the ones corresponding to a special type of lines), the numbers of lines through every point and of points lying on every line are obtained. This corresponds to the numbers of ones in columns and rows of the submatrices.
next article Construction of LDPC convolutional codes via difference triangle sets
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Metadata
Title
Twisted cubic and point-line incidence matrix in
Authors
Alexander A. Davydov
Stefano Marcugini
Fernanda Pambianco
Publication date
27-08-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 10/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00911-6

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