| 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 $PG(3,4)$. |
| DOI | 10.60063/GSU.FMI.106.11-24 |
| 2010 MSC | Primary: 51A20, 51A21, 94B65; Secondary: 51A22 |
| Attachment | Size |
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 106-011-024.pdf | 356.59 KB |