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In this paper, we generalize a result by Ball, Hill, Landjev and Ward on plane arcs to arcs with multiple points in spaces of arbitrary dimension. This result is further applied to the characterization of some non-Griesmer arcs in the 3-dimensional projective geometry over F4.

Hamada [Bull. Osaka Women’s Univ. 24:1–47, 1985; Discrete Math. 116:229-268, 1993] characterized the non-weighted minihypers having parameters ( ∑h i=1 vλi+1, ∑h i=1 vλi ; t, q) with t > λ1 > λ2 > · · · > λh ≥ 0. This result has been generalized in [Des. Codes Cryptogr. 45:123-138,2007] where it was proved that a weighted ( ∑h i=1 vλi+1, ∑h i=1 vλi ; t,… (More)

- Ivan N. Landjev, Assia Rousseva
- Electronic Notes in Discrete Mathematics
- 2017

- Ivan N. Landjev, Assia Rousseva, Leo Storme
- Des. Codes Cryptography
- 2016

Weintroduce the notion of t-quasidivisible arc as an (n, w)-arc inPG(k−1, q) such that every hyperplane has multiplicity congruent to n+ i modulo q , where i ∈ {0, 1, . . . , t}. We prove that every t-quasidivisible arc associated with a Griesmer code and satisfying an additional numerical condition is t times extendable.

- Ivan N. Landjev, Assia Rousseva
- Adv. in Math. of Comm.
- 2016

- Ivan N. Landjev, Assia Rousseva
- Electronic Notes in Discrete Mathematics
- 2017

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