# On resolvable Steiner 2-designs and maximal arcs in projective planes

@article{Tonchev2017OnRS, title={On resolvable Steiner 2-designs and maximal arcs in projective planes}, author={Vladimir D. Tonchev}, journal={Designs, Codes and Cryptography}, year={2017}, volume={84}, pages={165-172} }

A combinatorial characterization of resolvable Steiner 2-(v, k, 1) designs embeddable as maximal arcs in a projective plane of order $$(v-k)/(k-1)$$(v-k)/(k-1) is proved, and a generalization of a conjecture by Andries Brouwer (Geometries and groups, Springer, Heidelberg, 1981) is formulated.

## 5 Citations

### Maximal Arcs, Codes, and New Links Between Projective Planes of Order 16

- Mathematics, Computer ScienceElectron. J. Comb.
- 2020

The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes, and this phenomenon establishes new links between several of the known planes.

### Maximal arcs in projective planes of order 16 and related designs

- Mathematics
- 2018

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal…

### On partial geometries arising from maximal arcs

- MathematicsJournal of Algebraic Combinatorics
- 2021

The subject of this paper are partial geometries $$pg(s,t,\alpha )$$ p g ( s , t , α ) with parameters $$s=d(d'-1), \ t=d'(d-1), \ \alpha =(d-1)(d'-1)$$ s = d ( d ′ - 1 ) , t = d ′ ( d - 1 ) , α = (…

### A note on reducing the computation time for minimum distance and equivalence check of binary linear codes

- Computer ScienceArXiv
- 2018

The usability of the Gray code with constant weight words for computing linear combinations of codewords and the usefulness of combinatorial $2$-$(t,k,1)$ designs when there are memory limitations to the number of objects.

### On the classification of unitals on 28 points of low rank

- MathematicsApplicable Algebra in Engineering, Communication and Computing
- 2022

The classification of unitals with parameters 2-(28, 4, 1) according to the 2-rank of their incidence matrices was initiated by McGuire, Tonchev and Ward, who proved that the 2-rank of any unital on…

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