Translation Planes and Derivation Sets
E. F. Assmus,Jennifer D. Key +1 more
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Using ideas from algebraic coding theory, a general notion of aderivation set for a projective plane is introduced and certain geometric codes are used to locate such sets.Abstract:
Using ideas from algebraic coding theory, a general notion of aderivation set for a projective plane is introduced. Certain geometric codes are used to locate such sets. These codes also lead to upper bounds for thep-ranks of incidence matrices of translation planes in terms of the dimensions of the associated codes.read more
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Designs and their codes
TL;DR: The standard geometric codes are presented, followed by a list of recommended designs and some examples of how these designs might be implemented in the real world.
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Hadamard matrices and their designs: a coding-theoretic approach
E. F. Assmus,Jennifer D. Key +1 more
TL;DR: The notion of p-equivalence for Hadamard matrices has been studied in this paper, where the standard equivalence of Hadamards matrices is a refinement: for example, the sixty 24 x 24 matrices fall into six 2-equivalent classes.
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The moment map of a Lie group representation
TL;DR: In this article, the classical moment map of symplectic geometry is invoked to associate to a unitary representation of a Lie group G a G-invariant subset of the dual of the Lie algebra.
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An upper bound for the p -Rank of a translation plane
TL;DR: The summation term here is the p-rank of the affine geometry design A 2m,m(p) of points and m-flats in the 2m-dimensional vector space over F p.
References
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Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
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On the $p$-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes
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Affine and projective planes
E. F. Assmus,Jennifer D. Key +1 more
TL;DR: The notion of the hull of an affine plane π is introduced: the hull turns out to be the code generated, over an appropriate finite field F p , by all differences of those pairs of rows of an indicence matrix that represent parallel lines of π.