71 research outputs found
Classes of codes from quadratic surfaces of PG(3,q)
No full textWe examine classes of binary linear error correcting codes constructed from certain sets of lines defined relative to one of the two classical quadratic surfaces in . We give an overview of some of the properties of the codes, providing proofs where the results are new. In particular, we use geometric techniques to find small weight codewords, and hence, bound the minimum distance
A Note on Line-Baer subspace Partitions of PG(3, 4)
No full textWe consider the partitioning of PG(3, 4) into two types of objects, lines and Baer sub-3-spaces. Any such mixed partition gives rise to a spread of PG(7, 2) (and hence a projective plane of order 16) via a construction tech-nique given in [6]. The author has used the software package Magma to de-termine all such mixed partitions up to equivalence. It turns out that all of the translation planes of order 16 arise from one of the mixed partitions. Mathematics Subject Classification (2000): 51E2
Classical mixed partitions
No full textAbstractThrough a method given in Hirschfeld and Thas (General Galois Geometries, Oxford University Press, Oxford, 1991), a mixed partition of PG(2n−1,q2) can be used to construct a (2n−1)-spread of PG(4n−1,q) and, hence, a translation plane of order q2n. A mixed partition in this case is a partition of the points of PG(2n−1,q2) into PG(n−1,q2)'s and PG(2n−1,q)'s which we call Baer subspaces. In this paper, we completely classify the mixed partitions which generate regular spreads and, hence, can be classified as classical
Spreads, arcs, and multiple wavelength codes
No full textAbstractWe present several new families of multiple wavelength (2-dimensional) optical orthogonal codes (2D-OOCs) with ideal auto-correlation λa=0 (codes with at most one pulse per wavelength). We also provide a construction which yields multiple weight codes. All of our constructions produce codes that are either optimal with respect to the Johnson bound (J-optimal), or are asymptotically optimal and maximal. The constructions are based on certain pointsets in finite projective spaces of dimension k over GF(q) denoted PG(k,q)
Mixed partitions of PG(3,q2)
No full textAbstractA mixed partition of PG(2n−1,q2) is a partition of the points of PG(2n−1,q2) into (n−1)-spaces and Baer subspaces of dimension 2n−1. In (Bruck and Bose, J. Algebra 1 (1964) 85) it is shown that such a mixed partition of PG(2n−1,q2) can be used to construct a (2n−1)-spread of PG(4n−1,q) and hence a translation plane of order q2n. In this paper, we provide several new examples of such mixed partitions in the case when n=2
Corruption, Institutions and Regulation
No full textWe analyze the effects of corruption and institutional quality on the quality of business regulation. Our key findings indicate that corruption negatively affects the quality of regulation and that general institutional quality is insignificant once corruption is con- trolled for. These findings hold over a number of specifications which include additional exogenous historical and geographic controls. The findings imply that policy-makers should focus on curbing corruption to improve regulation, over wider institutional re- form.Business Regulation; Economic Policy; Institutional Quality; Corruption
On the number of -gons in finite projective planes
No full textLet denote a finite projective plane of order , and let be the bipartite point-line incidence graph of . For , let denote the number of cycles of length in . Are the numbers the same for all ? We prove that this is the case for by computing these numbers
Semiovals from Unions of Conics
No full textA semioval in a projective plane π is a collection of points O with the property that for every point P of O, there exists exactly one line of π meeting O precisely in the point P. There are many known constructions of and theoretical results about semiovals, especially those that contain large collinear subsets.
In a Desarguesian plane π a conic, the set of zeroes of some nondegenerate quadratic form, is an example of a semioval of size q+1 that also forms an arc (i.e., no three points are collinear). As conics are minimal semiovals, it is natural to use them as building blocks for larger semiovals. Our goal in this work is to classify completely the sets of conics whose union forms a semioval
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