In [9] the author proved that in characteristic 0 the jacobian J(C) = J(Cf ) of a hyperelliptic curve C = Cf : y 2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f ∈ K[x] is “very big”. Namely, if n = deg(f) ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then the ring ...

By its dual representation, a developable surface can be viewed as a curve of dual projective 3-space. After introducing an appropriate metric in the dual space and restricting ourselves to special parametrizations of the surfaces involved, we derive linear approximation algorithms for developable NURBS surfaces, including multiscale approximations. Special attention is paid to controlling the ...

H. Sato introduced a Schwarzian derivative of a contactomorphism of R 3 and and with T. Ozawa described its basic properties. In this note their construction is extended to all odd dimensions and to non-flat contact projective structures. The contact projective Schwarzian derivative of a contact projective structure is defined to be a cocycle of the contactomorphism group taking values in the s...

This problem was first suggested and discussed by Hale [6] and various special cases have been handled [ 5, 8, 121. As Hale observed, a partial linear space which is a projective plane with a point and all lines through it removed is merely the dual of an affine plane. In particular, the original projective plane can by synthetically reconstructed from the dual affine plane by the addition of a...

In this paper we present a new method for finding the weight enumerator of binary linear block codes by using genetic algorithms. This method consists in finding the binary weight enumerator of the code and its dual and to create from the famous MacWilliams identity a linear system (S) of integer variables for which we add all known information obtained from the structure of the code. The knowl...

We study the projective space S of rational parameter representations of degree d or less in real projective space P. The parameter representations of degree less than d form a special algebraic variety K1. We investigate the subspaces on K1 and their relation to rational curves in P, give a geometric characterization of the automorphism group of K1 and outline applications of the theory to pro...

A perfect code in a graph $$\Gamma $$ is subset C of $$V(\Gamma )$$ such that no two vertices are adjacent and every vertex ){\setminus } C$$ to exactly one C. Let G be finite group G. Then said if there exists Cayley admiting as code. It proved subgroup H only Sylow 2-subgroup This result provides way simplify the study codes general groups 2-groups. As an application, criterion for determinin...

In this note we offer a short summary of some recent results, to be contained in a forthcoming paper [4], on projective caps and linear error correcting codes arising from the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. More precisely, we consider the codes arising from the projective system determined by ε k (∆k) and determine some of their parameters. We also investigate special...