3,155 research outputs found
Classes of codes from quadratic surfaces of PG(3,q)
We examine classes of binary linear error correcting codes constructed from certain sets of lines defined relative to one of the two classical quadratic surfaces in . We give an overview of some of the properties of the codes, providing proofs where the results are new. In particular, we use geometric techniques to find small weight codewords, and hence, bound the minimum distance
Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps
Let Y be a surface with only finitely many singularities all of which are
cusps. A set of cusps on Y is called three-divisible, if there is a cyclic
global triple cover of Y branched precisely over these cusps. The aim of this
note is to determine the equations of surfaces of degrees carrying a minimal, non-empty, three-divisible set.Comment: 13 pages; a discussion of the family of quintics with 12
three-divisible cusps adde
Subspace code constructions
We improve on the lower bound of the maximum number of planes of mutually intersecting in at most one point leading to the following
lower bound: for
constant dimension subspace codes. We also construct two new non-equivalent
constant dimension subspace orbit-codes
Field reduction and linear sets in finite geometry
Based on the simple and well understood concept of subfields in a finite
field, the technique called `field reduction' has proved to be a very useful
and powerful tool in finite geometry. In this paper we elaborate on this
technique. Field reduction for projective and polar spaces is formalized and
the links with Desarguesian spreads and linear sets are explained in detail.
Recent results and some fundamental ques- tions about linear sets and scattered
spaces are studied. The relevance of field reduction is illustrated by
discussing applications to blocking sets and semifields
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