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Publication:3694152
zbMath0574.51001MaRDI QIDQ3694152
Publication date: 1985
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packingsspreadsquadricslinesspansHermitian surfacesovaloidstwisted cubicsk-capsk-arcscubic surfaces with 27 linesfinite projective spaces of three dimensions
Combinatorial aspects of finite geometries (05B25) General theory of linear incidence geometry and projective geometries (51A05) Other finite nonlinear geometries (51E25) Desarguesian and Pappian geometries (51A30) Research exposition (monographs, survey articles) pertaining to geometry (51-02)
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\(Af^*\). \(Af\) geometries, the Klein quadric and \({\mathcal H}^ n_ q\) ⋮ Classification of ovoids in \(PG(3,32)\) ⋮ \(m\)-systems of polar spaces ⋮ The lines of \(PG(4, 2)\) are the points on a quintic in \(PG(9, 2)\) ⋮ A characterization of the classical unital ⋮ Spreads and ovoids in finite generalized quadrangles ⋮ A characterisation of Thas maximal arcs in translation planes of square order ⋮ Intersection of arcs and normal rational curves in spaces of even characteristic ⋮ Ovoids of the quadric Q\((2n,q)\) ⋮ Primitive arcs in \(\mathrm{PG}(2,q)\) ⋮ On the 3-extendability of quaternary linear codes ⋮ Plane sections of Fermat surfaces over finite fields ⋮ Some maximal arcs in Hall planes ⋮ Space-filling subsets of a normal rational curve ⋮ Uniqueness of \([87,5,57; 3\)-codes and the nonexistence of \([258,6,171; 3]\)-codes] ⋮ A characterization of some \(\{ 3v_ 2+v_ 3,3v_ 1+v_ 2; 3,3\}\)-minihypers and some \([15,4,9; 3\)-codes with \(B_ 2=0\)] ⋮ A characterization of some \(\{ 3v_ 1+v_ 3,3v_ 0+v_ 2; 3,3\}\)-minihypers and its applications to error-correcting codes ⋮ On M.D.S. codes, arcs in PG(n,q) with q even, and a solution of three fundamental problems of B. Segre ⋮ Caps in finite projective spaces of odd order ⋮ Blocking sets of tangent and external lines to a hyperbolic quadric in \(\mathrm{PG}(3, q)\) ⋮ Partial flocks of quadratic cones with a point vertex in \(PG(n,q)\), \(n\) odd ⋮ Partial spreads over \({\mathbb{Z}}_ q\) ⋮ Some block designs associated with quadrics of PG(4,q) and PG(5,q) ⋮ Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes ⋮ Cyclic arcs and pseudo-cyclic MDS codes ⋮ Complete arcs ⋮ Small complete caps in \(PG(r,q)\), \(r\geq 3\) ⋮ Classical arcs in \(PG(r,q)\) for \(11\leq q\leq 19\) ⋮ On sets of type \((m,m+q)_2\) in \(\mathrm{PG}(3,q)\) ⋮ A note on maximal partial spreads with deficiency \(q+1\), \(q\) even ⋮ Counting generalized Reed-Solomon codes ⋮ Construction of asymmetric orthogonal arrays through finite geometries. ⋮ On saturating sets in projective spaces. ⋮ On \(k\)-caps in \(\mathrm{PG}(n, q)\), with \(q\) even and \(n \geq 4\) ⋮ Finite affine planes in projective spaces ⋮ Intriguing sets of quadrics in \(\mathrm{PG}(5, q)\) ⋮ The exterior splash in \(\mathrm{PG}(6, q)\): carrier conics ⋮ On \(k\)-caps in \(\mathrm{PG}(n, q)\), with \(q\) even and \(n \geq 3\) ⋮ The covering radius of \(\mathrm{PGL}(3, q)\) ⋮ Blocking sets of tangent and external lines to a hyperbolic quadric in \(\mathrm{PG}(3,q)\), \(q\) even ⋮ Embedding Steiner triple systems into Steiner systems \(S(2,4,v)\). ⋮ On the twisted cubic of \(\text{PG}(3, q)\) ⋮ Twisted tensor product group embeddings and complete partial ovoids on quadrics in \(\text{PG}(2^{t}-1,q)\). ⋮ A characterization of Hermitian curves ⋮ On minimum size blocking sets of the outer tangents to a hyperbolic quadric in \(\operatorname{PG}(3, q)\) ⋮ On a geometric representation of the subgroups of index 6 in \(S_ 6\) ⋮ Linear sections of the general linear group: A geometric approach ⋮ Sets in a finite plane with few intersection numbers and a distinguished point ⋮ On Buekenhout-Metz unitals of odd order ⋮ Completeness of the 95256-cap in \(\mathrm{PG}(12, 4)\) ⋮ Flocks of hyperbolic quadrics and linear groups containing homologies ⋮ Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen ⋮ On Buekenhout-Metz unitals of even order ⋮ A geometric construction of the Steiner system \(S(4,7,23)\) ⋮ Note on the existence of large minimal blocking sets in Galois planes ⋮ Ovoids of \(PG(3,16)\) are elliptic quadratics. II ⋮ A characterization of Hermitian varieties as codewords ⋮ The dimension of projective geometry codes ⋮ Translation nets: A survey ⋮ Complete \(k\)-arcs in PG(\(n,q\)), \(q\) even ⋮ Sum-free sets in vector spaces over \(GF(2)\) ⋮ On the construction of \([q^ 4+q^ 2-q, 5, q^ 4-q^ 3+q^ 2-2q; q\)-codes meeting the Griesmer bound] ⋮ Faserungen, die aus Reguli mit einem gemeinsamen Geradenpaar zusammengesetzt sind. (About spreads which are built up by reguli with two lines in common) ⋮ Configurations of weighted circles in finite inversive planes ⋮ On Buekenhout-Metz unitals in \(PG(2, q^ 2)\), \(q\) even ⋮ Completeness of normal rational curves ⋮ Maximal partial spreads and transversal-free translation nets ⋮ Caps in \(\mathrm{PG}(n,q)\), \(q\) even, \(n\ge 3\) ⋮ A characterization of Hadamard designs with SL\((2,q)\) acting transitively ⋮ A construction of some \([n,k,d;q\)-codes meeting the Griesmer bound] ⋮ On the size of a maximal partial spread ⋮ Classification of spreads of \(PG(3,4)\setminus PG(3,2)\) ⋮ Arcs and curves over a finite field ⋮ On the existence of abelian Hadamard difference sets and a new family of difference sets ⋮ On the spectrum of the values \(k\) for which a complete \(k\)-cap in \(PG(n,q)\) exists ⋮ \(\alpha\)-flocks with oval herds and monomial hyperovals ⋮ Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). I ⋮ Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). II ⋮ Caps in the projective geometry PG\((n,4)\) ⋮ Bruen chains over fields of small order ⋮ The construction of Cameron-Liebler line classes in \(PG(3,q)\) ⋮ A new semifield flock ⋮ Embeddings in Grassmannians ⋮ Surfaces in \(\mathbb{P}^5\) which do not admit trisecants ⋮ Unitals which meet Baer subplanes in 1 modulo \(q\) points ⋮ Mixed partitions of PG(3,\(q\)) ⋮ A combinatorial characterization of quadrics ⋮ Existence and non-existence of \(m\)-systems of polar spaces ⋮ Threefolds of the Klein quadric and trisecant lines ⋮ Computer search for small complete caps ⋮ The packing problem in statistics, coding theory and finite projective spaces ⋮ On the largest caps contained in the Klein quadric of \(PG(5,q)\), \(q\) odd ⋮ On nets of order \(q^ 2\) and degree \(q+1\) admitting GL(2,\(q\)) ⋮ Maximal subgroups of finite symplectic groups stabilizing spreads of lines. ⋮ Cyclic arcs in \(\mathrm{PG}(2,q)\) ⋮ Models and theorems of the classical circle planes ⋮ The classification of the largest caps in AG(5, 3) ⋮ \(k\)-arcs and dual \(k\)-arcs ⋮ Unitals in finite Desarguesian planes ⋮ On tangent spaces and external flats to Grassmannians of lines over finite fields ⋮ The packings of \(\mathrm{PG}(3,3)\) ⋮ Finite Cayley-Klein geometries. ⋮ On finite division algebras ⋮ Characterising pointsets in \(\mathrm{PG}(4,q)\) that correspond to conics ⋮ On the sharply 1-transitive subsets of \(PGL(2,p^ m)\) ⋮ Constructions and bounds for mixed-dimension subspace codes ⋮ Intersections in projective space. II: Pencils of quadrics ⋮ Saturated configurations of points in projective Galois spaces ⋮ On a set of lines of \(PG(3,q)\) corresponding to a maximal cap contained in the Klein quadric of \(PG(5,q)\). ⋮ Veronese subspace codes ⋮ Planar surfaces in positive characteristic ⋮ On the numerical range of matrices over a finite field ⋮ Lineare Geradenkomplexe über Schiefkörpern. (Linear complexes of lines over skew fields) ⋮ The 2-transitive ovoids ⋮ Conics, order, and k-arcs in AG(2,q) with q odd ⋮ Bicovering arcs and small complete caps from elliptic curves ⋮ Relative hemisystems on the Hermitian surface ⋮ Classification of the odd sets in \(\mathrm{PG}(4,4)\) and its application to coding theory ⋮ Collineation groups of translation planes admitting hyperbolic Buekenhout or parabolic Buekenhout-Metz unitals ⋮ A combinatorial characterization of the Hermitian surface ⋮ Perfect hash families of strength three with three rows from varieties on finite projective geometries ⋮ On translation spreads of \(H(q)\) ⋮ Cocliques in the Kneser graph on the point-hyperplane flags of a projective space ⋮ Slices of the unitary spread ⋮ Characterizing geometric designs. 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I: Combinatorics ⋮ Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG\((3,q)\) ⋮ Ovoids of \(\operatorname {PG}(3,q)\) stabilized by a central collineation ⋮ A model for the dual of the generalised hexagon \(H\)(\(q\)), \(q\) odd. ⋮ On cutting blocking sets and their codes ⋮ Quasimultiples of geometric designs ⋮ On the maximality of a set of mutually orthogonal sudoku Latin squares ⋮ Permutable polarities and a class of ovoids of the Hermitian surface ⋮ Piecewise regular spreads ⋮ Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture ⋮ Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG\((3,3^{2h+1})\) ⋮ The six semifield planes associated with a semifield flock ⋮ Two-character sets arising from gluings of orbits ⋮ Maximal partial spreads and the modular \(n\)-queen problem. II ⋮ Twisted cubic and plane-line incidence matrix in \(\mathrm{PG}(3,q)\) ⋮ Subspace code constructions ⋮ The flag-transitive symmetric designs with 45 points, blocks of size 12, and 3 blocks on every point pair ⋮ \(k\)-arcs and partial flocks ⋮ Optimal pseudo-cyclic codes and caps in \(PG(3,q)\) ⋮ Some inherited maximal arcs in derived dual translation planes ⋮ Construction of unitals in the Hall planes ⋮ Cyclic caps in \(\mathrm{PG}(3,q)\) ⋮ Generalized quadrangles of order \((q,q^ 2)\), \(q\) even, containing \(W(q)\) as a subquadrangle ⋮ On the classification of geometric codes by polynomial functions ⋮ The number of cubic surfaces with 27 lines over a finite field ⋮ Higgledy-piggledy sets in projective spaces of small dimension ⋮ Arcs in \(\mathrm{PG}(n,q)\) fixed by \(A_5\) and \(A_6\) ⋮ On the extendability of quaternary linear codes with four weights modulo 16 ⋮ The Eckardt point configuration of cubic surfaces revisited ⋮ The extended coset leader weight enumerator of a twisted cubic code ⋮ Ovoids in \(\text{PG}(3,q)\): A survey ⋮ In \(\mathrm{AG}(3, q)\) any \(q^2\)-set of class \([1, m, n_2\) is a cap] ⋮ On the \(\mathrm{PSU}(4,2)\)-invariant vertex-transitive strongly regular \((216, 40, 4, 8)\) graph ⋮ Spreads admitting net generating regulizations ⋮ Tangent sets in finite spaces ⋮ In \(\mathrm{AG}(3,q)\) any \(q^2\)-set of class \([0,m,n_2\) containing a line is a cylinder] ⋮ A characterization of the non-Baer lines of a Hermitian surface ⋮ A characterization of the finite Veronesean by intersection properties ⋮ Clifford parallelism: old and new definitions, and their use ⋮ A note on sets of type \((0, mq, 2mq)_2\) in \(PG(3, q)\) ⋮ Evaluation codes from smooth quadric surfaces and twisted Segre varieties ⋮ Divisible arcs, divisible codes, and the extension problem for arcs and codes ⋮ A characterization of the family of secant lines to a hyperbolic quadric in \(\mathrm{PG} ( 3 , q )\), \(q\) odd ⋮ Divisible designs, Laguerre geometry, and beyond ⋮ On independent star sets in finite graphs ⋮ A combinatorial characterization of the Baer and the unital cone in \(\mathrm{PG}(3,q^2)\) ⋮ On the minimum size of complete arcs and minimal saturating sets in projective planes ⋮ Small complete caps in three-dimensional Galois spaces ⋮ A characterisation of the planes meeting a non-singular quadric of \(\mathrm{PG}(4,q)\) in a conic ⋮ Caps in \(\mathrm{PG}(n,q)\) with \(q\) even and \(n\geq 3\) ⋮ A new family of extended generalized quadrangles of order \((q+1,q-1)\) ⋮ The determination of ovoids of PG(3,\(q\)) containing a pointed conic ⋮ Twisted cubic and point-line incidence matrix in \(\operatorname{PG}(3,q)\) ⋮ Graphs cospectral with \(\operatorname{NU}(n + 1,q^2)\), \(n \neq 3\) ⋮ PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of \(\mathrm{PG}(5,2)\) ⋮ Structure of a code related to \(\mathrm{Sp}(4,q)\), \(q\) even ⋮ A construction for infinite families of semisymmetric graphs 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external lines to an elliptic quadric in \(\mathrm{PG}(3,q)\) ⋮ Two characterizations of the family of secant lines of an ovoid of \(\mathrm{PG}(3,q)\) ⋮ On regular systems of finite classical polar spaces ⋮ On line covers of finite projective and polar spaces ⋮ Classification of maximal caps in PG(3,5) different from elliptic quadrics ⋮ The automorphism group of \(NU(3,q^2)\) ⋮ Blocking sets of certain line sets related to a hyperbolic quadric in \(\mathrm{PG}(3, q)\) ⋮ The tangent splash in \(\mathrm{PG}(6, q)\) ⋮ A new family of relative hemisystems on the Hermitian surface ⋮ Parallelisms of \(\mathrm{PG}(3,4)\) invariant under an elementary abelian group of order 4 ⋮ Smooth cubic surfaces with 15 lines ⋮ On small line sets with few odd-points ⋮ Cameron-Liebler line classes with parameter \(x = \frac{q^2 - 1}{2}\) ⋮ A characterization of the family of secant lines to a hyperbolic quadric in \(\mathrm{PG}(3,q)\), \(q\) odd. 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the planes meeting a hyperbolic quadric of $\PG(3,q)$ in a conic ⋮ On the non-trivial minimal blocking sets in binary projective spaces ⋮ On \(\alpha \)-points of \(q\)-analogs of the Fano plane ⋮ Quadratic sets on the Klein quadric ⋮ Nonsingular cubic surfaces over F2k ⋮ Orbits of lines for a twisted cubic in \(\mathrm{PG}(3, q)\) ⋮ Orbits of the class \(\mathcal{O}_6\) of lines external to the twisted cubic in \(\mathrm{PG}(3, q)\) ⋮ On the geometry of a \((q+1)\)-arc of \(\mathrm{PG}(3,q)\), \(q\) even ⋮ Rational points on cubic surfaces and AG codes from the norm-trace curve ⋮ Exponentially larger affine and projective caps ⋮ A modular equality for m$m$‐ovoids of elliptic quadrics ⋮ Upper bounds on the length function for covering codes with covering radius \(R\) and codimension \(tR+1\) ⋮ Incidence matrices for the class \({\mathcal{O}}_6\) of lines external to the twisted cubic in \(\mathrm{PG}(3,q)\) ⋮ Sets of type \((q+2,n)\) in \(\mathrm{PG}(3, q)\) ⋮ Identifying codes for generalized quadrangles ⋮ Suzuki-Tits ovoids through the years ⋮ A characterisation of \(\mathbb{F}_q\)-conics of \(\mathrm{PG}(2,q^3)\) ⋮ On large partial ovoids of symplectic and Hermitian polar spaces ⋮ Nonsingular hypercubes and nonintersecting hyperboloids ⋮ On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces ⋮ Geometry of smooth extremal surfaces ⋮ On near-MDS codes and caps ⋮ The main conjecture for MDS codes ⋮ External points to a conic from a Baer subplane ⋮ A classification of flag-transitive \(2\)-\((k^2, k, \lambda)\) designs with \(\lambda\mid k\) ⋮ Space sextic curves with six bitangents, and some geometry of the diagonal cubic surface ⋮ Unnamed Item ⋮ The Axiomatic Destiny of the Theorems of Pappus and Desargues ⋮ Unnamed Item ⋮ Regular hyperbolic fibrations ⋮ A combinatorial characterization of two skew lines ⋮ A combinatorial characterization of parabolic quadrics ⋮ Caps on classical varieties and their projections ⋮ Maximal arcs in projective three-spaces and double-error-correcting cyclic codes ⋮ The Hermitian null-range of a matrix over a finite field ⋮ Singer line orbits in \(\text{PG} (3,q)\) ⋮ The geometric description of a cyclic \((q- \sqrt{q}+1)\)-arc in \(\text{PG} (q-\sqrt{q}-3,q)\), \(q\) square ⋮ Groups of maximal arcs ⋮ Subquadrangles of generalized quadrangles of order \((q^2,q)\), \(q\) even ⋮ Minimal covers of the Klein quadric ⋮ Packing and covering groups with subgroups ⋮ On the geometry of Hermitian matrices of order three over finite fields ⋮ A four-class association scheme ⋮ Constructions of biangular tight frames and their relationships with equiangular tight frames ⋮ Hyperflock determining line sets and totally regular parallelisms of \(\text{PG}(3,\mathbb{R})\) ⋮ Trivectors yielding spreads in PG\((5,2)\) ⋮ Hemisystems of \(\mathcal{Q}(6,q)\), \(q\) odd ⋮ On subspace codes ⋮ Tangency sets inPG(3, q) ⋮ Automorphisms of cubic surfaces in positive characteristic ⋮ Explicit Determination of 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