منابع مشابه
Translation Planes and Derivation Sets
Using ideas from algebraic coding theory, a general notion of a derivation set for a pro-jective plane is introduced. Certain geometric codes are used to locate such sets. These codes also lead to upper bounds for the pranks of incidence matrices of translation planes in terms of the dimensions of the associated codes.
متن کاملDual Codes of Translation Planes
We improve on the known upper bound for the minimum weight of the dual codes of translation planes of certain orders by providing a general construction of words of small weight. We use this construction to suggest a possible formula for the minimum weight of the dual p-ary code of the desarguesian plane of order pm for any prime p and any m ≥ 1.
متن کاملThe Construction of Translation Planes
Can eve.ry (non-Desarguest.. an) projee.,tJVe p~' ~ imbedded (in some natural, g~anet.ric ff.hion) in af1J8sarguesian) projective space? The Ite,titn is ne...WI~.ut .. ,trnp .. · ortant, for, if the answer is yes, tfo entirely SEijifia'Wt fields of research can be united~ 1his paper ;p~1des. conceptually simple geometric construction 1vh1dti',Y1elds an affirmative answer for a broad class of pl...
متن کاملA family of translation planes
An infinite family of non-Desarguesian translation planes of order q with kernel GF(q) is constructed, for any odd prime power q. The collineation group of each plane has orbits of lengths 1, q, and q − q on the translation line. The method used for the construction is net replacement, starting from a Dickson-Knuth semifield plane. The planes are constructed via spreads and the spreads via spre...
متن کاملOrthogonal spreads and translation planes
There have been a number of striking new results concerning translation planes of characteristic 2, obtained using orthogonal and symplectic spreads. The impetus for this came from coding theory. This paper surveys the geometric advances, while providing a hint of their coding{theoretic connections.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1985
ISSN: 0025-5645
DOI: 10.2969/jmsj/03710157