<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

On Almost Complete Caps in PG(<italic>N</italic>, <italic>q</italic>)

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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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 ≥...

On Almost Complete Caps in PG(N, q)

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
Projective space, complete cap, complete arc, almost complete cap, almost complete arc

© 2018 Alexander A. Davydov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Almost Complete Caps in PG(N, q)

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

KeywordsProjective space, complete cap, complete arc, almost complete cap, almost complete arc

© 2018 Alexander A. Davydov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Projective space, complete cap, complete arc, almost complete cap, almost complete arc