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Kestenband proved in [12] that there are only seven pairwise non‐isomorphic Hermitian intersections in the desarguesian projective plane PG(2, q) of square order q. His classification is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be projectively equivalent in PG(2, q) and might have different collineation groups. The projective classification of Hermitian intersections in PG(2, q) is the main goal in this paper. It turns out that each of Kestenband's classes consists of projectively equivalent Hermitian intersections. A complete classification of the linear collineation groups preserving a Hermitian intersection is also given. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 445–459, 2001 相似文献
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The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes-characterised by admitting a sparse parity check matrix-with good correction capabilities. In the present paper the orbits of subspaces of a finite projective space under the action of a Singer cycle are investigated. The incidence matrix associated to each of these structures yields an LDPC code in a natural manner. 相似文献
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In this article we construct new minimal intersection sets in \(\mathrm {AG}(r,q^2)\) sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in \(\mathrm {PG}(r,q^2)\) with r even and we also compute their weight distribution. 相似文献
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Suppose to be a subgraph of a graph . We define a sampling of a -design into a -design as a surjective map mapping each block of into one of its subgraphs. A sampling will be called regular when the number of preimages of each block of under is a constant. This new concept is closely related with the classical notion of embedding, which has been extensively studied, for many classes of graphs, by several authors; see, for example, the survey by Quattrocchi (2001) [29]. Actually, a sampling might induce several embeddings of the design into , although the converse is not true in general. In the present paper, we study in more detail the behaviour of samplings of -complete designs of order into -complete designs of the same order and show how the natural necessary condition for the existence of a regular sampling is actually sufficient. We also provide some explicit constructions of samplings, as well as propose further generalisations. 相似文献
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Denote by \({{\mathcal {G}}}_k(V)\) the Grassmannian of the k-subspaces of a vector space V over a field \({\mathbb {K}}\). There is a natural correspondence between hyperplanes H of \({\mathcal {G}}_k(V)\) and alternating k-linear forms on V defined up to a scalar multiple. Given a hyperplane H of \({{\mathcal {G}}_k}(V)\), we define a subspace \(R^{\uparrow }(H)\) of \({{\mathcal {G}}_{k-1}}(V)\) whose elements are the \((k-1)\)-subspaces A such that all k-spaces containing A belong to H. When \(n-k\) is even, \(R^{\uparrow }(H)\) might be empty; when \(n-k\) is odd, each element of \({\mathcal {G}}_{k-2}(V)\) is contained in at least one element of \(R^{\uparrow }(H)\). In the present paper, we investigate several properties of \(R^{\uparrow }(H)\), settle some open problems and propose a conjecture. 相似文献
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Luca Giuzzi 《Results in Mathematics》2006,49(1-2):81-88
Multiple derivation of the classical ovoid of the Hermitian surface
of
is a well known, powerful method for constructing large families of non classical ovoids of
. In this paper, we shall provide a geometric costruction of a family of ovoids amenable to multiple derivation. 相似文献
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We present a new construction of non-classical unitals from a classical unital U in . The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of with the following three properties:
- (i)
- points of Π are those of ;
- (ii)
- lines of Π are certain lines and conics of ;
- (iii)
- the points in U form a non-classical B-M unital in Π.
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Using geometric properties of the variety ${\mathcal V_{r,t}}$ , the image under the Grassmannian map of a Desarguesian (t ? 1)-spread of PG(rt ? 1, q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We determine the precise parameters of these codes and characterise the words of minimum weight. 相似文献