# On the structure of some arcs related to caps and the nonexistence of some optimal codes

 Title On the structure of some arcs related to caps and the nonexistence of some optimal codes Publication Type Journal Article Year of Publication 2019 Authors Rousseva A Journal Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique Volume 106 Start Page 11 Pagination 11-24 ISSN 1313-9215 (Print) 2603-5529 (Online) Keywords nite projecive geometries, arcs, extendable arcs, Griesmer arcs, Griesmer codes, Linear codes, the griesmer bound Abstract In this paper we solve two instances of the main problem in coding theory for linear codes of dimension 5 over $\mathbb{F}_4$. We prove the nonexistence of $[395,5,295]_4$- and $[396,5,296]_4$-codes which implies the exact values $n_4(5,295)=396$ and $n_4(5,296)=397$. As a by-product, we characterize the arcs with parameters $(100,26)$ in $PG(3,4)$. 2010 MSC Primary: 51A20, 51A21, 94B65; Secondary: 51A22
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