We survey recent results on p-ranks of certain inclusion matrices arising from a finite projective space or a finite symplectic space. 2000 Mathematics Subject Classification: 05E20, 20G05, 20C33.

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction. AMS subject classification: 05E20, 05B25, 11T71, 94B25, 94B27, 51E22, 51E20, 20G40, 14L35

We give a general construction for unitals of order q admitting an action of SU(2, q). The construction covers the classical hermitian unitals, Grüning’s unitals in Hall planes and at least one unital of order four where the translation centers fill precisely one block. For the latter unital, we determine the full group of automorphisms and show that there are no group-preserving embeddings int...

In this paper we study embeddings of the Fano plane as a bipartite graph. We classify all possible embeddings especially focusing on those with non-trivial automorphism group. We study them in terms of rotation systems, isomorphism classes and chirality. We construct quotients and show how to obtain information about face structure and genus of the covering embedding. As a by-product of the cla...

Let Fn q be a vector space of dimension n over the finite field Fq . A q-analog of a Steiner system (also known as a q-Steiner system), denoted Sq(t,k,n), is a set S of k-dimensional subspaces of Fn q such that each t-dimensional subspace of Fn q is contained in exactly one element of S . Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k= n. In this pap...

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...

In this paper, we consider the projective special linear group $PSL_2(59)$ and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$. Moreover, we obtain parameters of these designs and their automorphism groups. It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.

The study of rhythmic canons by mathematicians with musical interest has given rise to unexpected connections to non trivial mathematical problems. The author tried a new approach based on a Galoisian interpretation of the novel results and concepts of Coven and Meyerowitz [4]. Extending this in a second part to finite fields, he concludes with unexpected results. 1 Rhythmic canons, tiling the ...