Journal ArticleDOI
Planes of order n with collineation groups of order n 2
Peter Dembowski,T. G. Ostrom +1 more
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This article is published in Mathematische Zeitschrift.The article was published on 1968-06-01. It has received 265 citations till now. The article focuses on the topics: Collineation & Order (group theory).read more
Citations
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Planar Functions and Planes of Lenz-Barlotti Class II
TL;DR: Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes, and which cannot be obtained by derivation or lifting.
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A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing
Kelan Ding,Cunsheng Ding +1 more
TL;DR: In this article, a class of two-weight and three-weight linear codes over GF(p) was constructed, and their application in secret sharing was investigated, and some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear codes.
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A family of skew Hadamard difference sets
Cunsheng Ding,Jin Yuan +1 more
TL;DR: A family of new perfect nonlinear functions are presented, and it is shown that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamards difference sets.
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Permutation polynomials over finite fields - A survey of recent advances
TL;DR: This work surveys the contributions made to permutation polynomials over finite fields in recent years and places emphasis on significant results and novel methods.
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The weight distribution of a class of linear codes from perfect nonlinear functions
TL;DR: In this correspondence, the weight distribution of a class of linear codes based on perfect nonlinear functions (also called planar functions) is determined and are either optimal or among the best codes known.
References
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Book
The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.
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Ovals in a finite projective plane
TL;DR: In this paper, the authors consider a projective space of dimension 2 over a Galois field γ and show that every straight line and every non-singular conic of γ has at most q + 1 points.
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The Nonexistence of Certain Finite Projective Planes
R. H. Bruck,H. J. Ryser +1 more
TL;DR: A projective plane geometry π is a mathematical system composed of undefined elements called points and undefined sets of points (at least two in number) called lines, subject to the following three postulates: (P1) Two distinct points are contained in a unique line; (P2) two distinct lines contain a unique common point; and (P3) each line contains at least three points.
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Projectivities with fixed points on every line of the plane
TL;DR: In this paper, a survey of the quasi-perspectivities in Desarguesian projective planes is presented, where the authors show that every line in a projectivity has at least two fixed points on a fixed line.
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Polarities in finite projective planes
TL;DR: In this paper, it was shown that there are always at least n+1 absolute points lying on their polars in a regular projective plane, and that the existence of hyperbolic polarities is not necessary.