ON THE STRUCTURE OF (t mod q)-ARCS IN FINITE PROJECTIVE GEOMETRIES

Authors

  • Assia P. Rousseva

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 $\mathbb{F}_5$.

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Published

2016-12-12

How to Cite

P. Rousseva, A. (2016). ON THE STRUCTURE OF (t mod q)-ARCS IN FINITE PROJECTIVE GEOMETRIES. Ann. Sofia Univ. Fac. Math. And Inf., 103, 5–22. Retrieved from https://ftl5.uni-sofia.bg/index.php/fmi/article/view/48

Issue

Vol. 103 (2016): Ann. Sofia Univ. Fac. Math and Inf.

Section

Articles