The Mathieu group and its pseudogroup extension .
The maximum size of a partial spread in is .
The minimum rank problem over finite fields.
The minimum size of complete caps in .
The nonexistence of certain projective planes of order 15.
The Nonexistence of some Griesmer Arcs in PG(4, 5)
In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.
The n-point-invariants of the projective line and cross-ratios of n-tuples
The nuclei and other properties of -primitive semifield planes.
The rank 2 geometries of the simple Suzuki groups .
The residually weakly primitive geometries of .
The Translation Planes of Order 16 that Admit Nonsolvable Collineation Groups.
The tree of life and other affine buildings.
The triangular extensions of a generalized quadrangle of order .
The uniqueness of groups of type J4.
The universal embedding of the near polygon .
The valuations of the near octagon .
The valuations of the near polygon G.
The Veldkamp space of two-qubits.
The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
We study the functional codes defined on a projective algebraic variety , in the case where is a non-degenerate Hermitian surface. We first give some bounds for , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code .
Three amalgams of A_5