Cybernetics and Information Technologies
Special Thematic Issue on Optimal Codes and Related Topics
About this article
Published Online: May 26, 2018
Page range: 54 - 62
Received: Sep 25, 2017
Accepted: Dec 01, 2017
DOI: https://doi.org/10.2478/cait-2018-0020
Keywords
© 2018 Alexander A. Davydov et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
We propose the concepts of almost complete subset of an elliptic quadric in the projective space PG(3, q) and of almost complete cap in the space PG(N, q), N ≥ 3, as generalizations of the concepts of almost complete subset of a conic and of almost complete arc in PG(2, q). Upper bounds of the smallest size of the introduced geometrical objects are obtained by probabilistic and algorithmic methods.