The non-existence of $(104,22;3,5)$-arcs

Ivan Landjev; Assia  Rousseva

doi:10.3934/amc.2016029

Article Contents

2016, Volume 10, Issue 3: 601-611. Doi: 10.3934/amc.2016029

This issue Previous Article Explicit constructions of some non-Gabidulin linear maximum rank distance codes Next Article Further results on multiple coverings of the farthest-off points

The non-existence of $(104,22;3,5)$-arcs

Ivan Landjev^1, and
Assia Rousseva^2,

1.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. bl. 8, Sofia 1113
2.
Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier blvd., 1164 Sofia

Received: April 30, 2015

Revised: August 31, 2015

Published: July 2016

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Abstract

Using some recent results about multiple extendability of arcs and codes, we prove the nonexistence of $(104,22)$-arcs in $PG(3,5)$. This implies the non-existence of Griesmer $[104,4,82]_5$-codes and settles one of the four remaining open cases for the main problem of coding theory for $q=5,k=4,d=82$.

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Mathematics Subject Classification: Primary: 51C05, 51E21, 51E22; Secondary: 94B05.

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