Extension of Cap by Size and Degree in the Space PG(3,11)‎

Authors

Jabbar Sharif Radhi Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
Emad Bakr Al-Zangana Department of Mathematics, College of Science,Mustansiriyah University, Baghdad, Iraq.

DOI:

https://doi.org/10.30526/36.2.3025

Keywords:

Cap, Complete (Incomplete) cap, Companion matrix, Projective space, τ_i- distribution, c_i-distribution.

Abstract

A cap of size and degree in a projective space, (briefly; (k,r)-cap) is a set of points with the property that each line in the space meet it in at most points. The aim of this research is to extend the size and degree of complete caps and incomplete caps, (k, r)-caps of degree r<12 in the finite projective space of dimension three over the finite field of order eleven, which already exist and founded by the action of subgroups of the general linear group over the finite field of order eleven and degree four, to (k+i,r+1) -complete caps. These caps have been classified by giving the t_i-distribution and -distribution. The Gap programming has been used to execute the designed algorithms and computations.

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