1,720,981 research outputs found
Symplectic semifield spreads of PG(5, qt), q even
No full textLet q > 2·34t be even. We prove that the only symplectic semifield spread of PG(5, qt), whose associate semifield has center containing Fq, is the Desarguesian spread. Equivalently, a commutative semifield of order q3t, with middle nucleus containing Fqt and center containing Fq, is a field. We do that by proving that the only possible Fq-linear set of rank 3t in PG(5, qt) disjoint from the secant variety of the Veronese surface is a plane of PG(5, qt)
LDPC codes from the Hermitian curve
Full text linkIn this paper, we study the code C which has as parity check matrix H the incidence matrix of the design of the Hermitian curve and its (q + 1)-secants. This code is known to have good performance with an iterative decoding algorithm, as shown by Johnson and Weller in ( Proceedings at the ICEE Globe com conference, Sanfrancisco, CA, 2003). We shall prove that C has a double cyclic structure and that by shortening in a suitable way H it is possible to obtain new codes which have higher code-rate. We shall also present a simple way to constructing the matrix H via a geometric approach
Lax embeddings of the Hermitian unital
No full textIn this paper, we prove that every lax generalized Veronesean embedding of the Hermitian unital of a quadratic extension of the field and , in a , with any field and d a parts per thousand yen 7, such that disjoint blocks span disjoint subspaces, is the standard Veronesean embedding in a subgeometry of (and d = 7) or it consists of the projection from a point of from a subgeometry of into a hyperplane . In order to do so, when we strongly use the linear representation of the affine part of (the line at infinity being secant) as the affine part of the generalized quadrangle (the solid at infinity being non-singular); when , we use the connection of with the generalized hexagon of order 2
On the algebraic variety Vr,t
Full text linkAbstractThe variety Vr,t is the image under the Grassmannian map of the (t−1)-subspaces of PG(rt−1,q) of the elements of a Desarguesian spread. We investigate some properties of this variety, with particular attention to the case r=2: in this case we prove that every t+1 points of the variety are in general position and we give a new interpretation of linear sets of PG(1,qt)
Families of twisted tensor product codes
No full textUsing geometric properties of the
variety \cV_{r,t}, the image
under the Grassmannian map
of a Desarguesian -spread of \PG(rt-1,q),
we introduce error correcting codes related to
the twisted tensor product construction, producing several families of
constacyclic codes. We determine the precise
parameters of these codes and
characterise the words of minimum weight
On symplectic semifield spreads of PG(5,q2), q odd
Full text linkWe prove that there exist exactly three non-equivalent symplectic semifield spreads of PG ( 5 , q2), for q2> 2 .38odd, whose associated semifield has center containing Fq. Equivalently, we classify, up to isotopy, commutative semifields of order q6, for q2> 2 .38odd, with middle nucleus containing q2Fq2and center containing q Fq
Asymptotic improvements to the lower bound of certain bipartite Turán numbers
Full text linkWe show that there are graphs with n vertices containing no K-5,K-5 which have about 1/2n(7/4) edges, thus proving that ex(n, K-5,K-5) >= 1/2(1 + o(1))n(7/4). This bound gives an asymptotic improvement to the known lower bounds on ex(n, K-t,K-s) for t = 5 when 5 <= s <= 12, and t = 6 when 6 <= s <= 8
On symplectic semifield spreads of PG(5,q2), q even
No full textWe prove that the only symplectic semifield spreads of PG(5,q^2), q>= 2^14, even, whose associated semifield has center containing F_q, is the Desarguesian spread, by proving that the only F_q-linear set of rank 6 disjoint from the secant variety of the Veronese surface of PG(5,q^2) is a plane with three points of the Veronese surface PG(5,q^6)\PG(5,q^2)
The use of blocking sets in Galois geometries and in related research areas
Full text linkBlocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers to investigate the problems that can be solved by using blocking sets. By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems
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