منابع مشابه
Finite 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...
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Preface The book in front of you represents my work as a PhD student. Using the word 'work' in this context is not really appropriate. During the past three years, I never had the feeling to 'work', but rather to play around with various structures, to have fun trying to prove theorems and to enjoy discovering just a tiny bit of the enormous mathematical world. This thesis is a structured way o...
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In this article we shall prove that, for q = p prime and roughly 3 8 -th’s of the values of d < q k−1, there is no linear code meeting the Griesmer bound. This result uses Blokhuis’ theorem on the size of a t-fold blocking set in PG(2, p), p prime, which we generalise to higher dimensions. We also give more general lower bounds on the size of a t-fold blocking set in PG(δ, q), for arbitrary q a...
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Let AR,q denote a family of covering codes, in which the covering radius R and the size q of the underlying Galois field are fixed, while the code length tends to infinity. The construction of families with small asymptotic covering densities is a classical problem in the area Covering Codes. In this paper, infinite sets of families AR,q, where R is fixed but q ranges over an infinite set of pr...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.04.007