منابع مشابه
Linear codes from projective spaces
The linear code Cs,t(n, q) of s-spaces and t-spaces in a projective space PG(n, q), q = ph, p prime, is defined as the vector space spanned over Fp by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970’s. In this paper, we give an overview of what is currently know...
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In this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings. Also, it is shown that any linear space of order c can be embedded in a linear space of order about 13v in which there are no lines of size 2.
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The aim of this paper is to settle a question about the partitioning of the projective plane by lines except for a small set. Suppose that Q is a set of points in the projective plane of order n and 6 is a set of lines that partitions the complement of Q. If Q has at most 2n&1 points and P has less than n+1+n lines, then these lines are concurrent. An example is given which shows that the condi...
متن کاملFinite linear spaces and projective planes
In 1948, De Bruijn and Erdös proved that a finite linear space on v points has at least v lines, with equality occurring if and only if the space is either a near-pencil (all points but one collinear) or a projective plane . In this paper, we study finite linear spaces which are not near-pencils . We obtain a lower bound for the number of lines (as a function of the number of points) for such l...
متن کاملEmbedding the Linear Structure of Planar Spaces into Projective Spaces
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00402-2