| Title | ON THE STRUCTURE OF (t mod q)-ARCS IN FINITE PROJECTIVE GEOMETRIES |
| Publication Type | Journal Article |
| Year of Publication | 2016 |
| Authors | Rousseva A |
| Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
| Volume | 103 |
| Pagination | 5-22 |
| ISSN | 0205-0808 |
| Keywords | arcs, blocking sets, divisible arcs, extendable arcs, finite projective geometries, minihypers, quasidivisible arcs, the griesmer bound |
| Abstract | In this paper, we introduce constructions and structure results for (t mod q)-arcs. We prove that all (2 mod q)-arcs in PG(r, q) with $r \geq 3$ are lifted. We find all (3 mod 5) plane arcs of small cardinality not exceeding 33 and prove that every (3mod 5)-arc in PG(3, 5) of size at most 158 is lifted. This result is applied further to rule out the existence of (104, 22)-arcs in PG(3, 5) which solves an open problem on the optimal size of fourdimensional linear codes over $\mathbb{F}_5$. |
| 2000 MSC | Main 51A20, 51A21, 51A22, Secondary 94B65 |
| Attachment | Size |
|---|---|
 103-005-022.pdf | 231.06 KB |