We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.
Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...
We shall compute the exact value of rigidity of the triangular matrix with entries 0 and 1.
Les -plans (définis ci-dessous) ont été introduits dans [1]. Leur étude englobe celle des plans affines et projectifs finis, des familles de carrés latins deux à deux orthogonaux, de certains plans équilibrés et partiellement équilibrés . La question de leur existence est très mal connue, celle de leur unicité n’a pratiquement pas été abordée. Nous nous proposons de montrer le théorème suivant : pour qu’il existe un -plan il est nécessaire que : soient entiers.
We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer,...
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of mutually orthogonal Latin squares of order to construct a set of mutually orthogonal Latin squares of order .
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed -minors.