3,155 research outputs found

    Classes of codes from quadratic surfaces of PG(3,q)

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    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 PG(3,q)PG(3,q). 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

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    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 Y⊂P3Y \subset P_3 of degrees ≀6\leq 6 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

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    We improve on the lower bound of the maximum number of planes of PG(8,q){\rm PG}(8,q) mutually intersecting in at most one point leading to the following lower bound: Aq(9,4;3)≄q12+2q8+2q7+q6+q5+q4+1{\cal A}_q(9, 4; 3) \ge q^{12}+2q^8+2q^7+q^6+q^5+q^4+1 for constant dimension subspace codes. We also construct two new non-equivalent (6,(q3−1)(q2+q+1),4;3)q(6, (q^3-1)(q^2+q+1), 4; 3)_q constant dimension subspace orbit-codes

    Field reduction and linear sets in finite geometry

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    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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