Generalized Forder method and translation planes [Lecture]
نویسندگان
چکیده
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 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.
متن کاملGeneralized j-planes
We construct and study a class of translation planes with kernel K ∼= GF (q), order q, and n > 2. These planes generalize the j-planes discovered by Johnson, Pomareda and Wilke in [14]. We show these planes are actually jj · · · j-planes. Hence, most of the results obtained in this article are on jj · · · j-planes. In fact, our study shows that these planes are either nearfield or new. An infin...
متن کاملGeneralized Principal Planes
ABSTRACT We introduce a statistical method for the decomposition of data sets into planes. With the help of principal component analysis or factor analysis the data are presented in a lower-dimensional space. The factors spanning this new co-ordinate system are rotated afterwards in that sense to fulfill the idea of simple structure, extended to two dimensions. The resulting planes which are sp...
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.
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1960
ISSN: 0528-2195
DOI: 10.21136/cpm.1960.108115