The minimum order of complete caps in $PG(4,4)$

Daniele Bartoli; Alexander A. Davydov; Stefano Marcugini; Fernanda Pambianco

doi:10.3934/amc.2011.5.37

Article Contents

2011, Volume 5, Issue 1: 37-40. Doi: 10.3934/amc.2011.5.37

This issue Previous Article Construction of self-dual codes with an automorphism of order $p$ Next Article From skew-cyclic codes to asymmetric quantum codes

The minimum order of complete caps in $PG(4,4)$

1.
Department of Mathematics and Informatics, Perugia University, Perugia, 06123
2.
Institute for Information Transmission Problems (Kharkevich institute), Russian Academy of Sciences, GSP-4, Moscow, 127994

Received: March 31, 2010

Revised: November 30, 2010

Published: January 2011

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Abstract

It has been verified that in $PG(4,4)$ the smallest size of complete caps is 20 and that the values from 20 to 41 form the spectrum of possible sizes of complete caps. This result has been obtained by a computer-based proof helped by the non existence of some codes.

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Mathematics Subject Classification: Primary: 51E21, 51E22; Secondary: 94B05.

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References

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