The packing problem in statistics, coding theory and finite projective spaces
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Publication:1299059
DOI10.1016/S0378-3758(98)00043-3zbMath0958.51013WikidataQ127088957 ScholiaQ127088957MaRDI QIDQ1299059
J. W. P. Hirschfeld, Storme, L.
Publication date: 28 January 2001
Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)
Spreads and packing problems in finite geometry (51E23) Combinatorial structures in finite projective spaces (51E20) Research exposition (monographs, survey articles) pertaining to geometry (51-02)
Related Items (36)
Projective planes and congestion-free networks ⋮ Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search ⋮ Complete \((k,3)\)-arcs from quartic curves ⋮ Some constructions of quantum MDS codes ⋮ A geometric approach to classifying Griesmer codes ⋮ On critical exponents of Dowling matroids ⋮ Caps in finite projective spaces of odd order ⋮ Complete arcs and caps in some papers of Giuseppe Tallini and Walking with Giuseppe Tallini along the streets of ``Augusta Perusia ⋮ Complete \((k,4)\)-arcs from quintic curves ⋮ On complete \(m\)-arcs ⋮ Algebraic constructions of complete \(m\)-arcs ⋮ Detecting arrays for effects of single factors ⋮ Constructing heterogeneous hash families by puncturing linear transversal designs ⋮ On saturating sets in projective spaces. ⋮ On the minimum number of minimal codewords ⋮ New upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane ⋮ Conics and caps ⋮ On sizes of complete arcs in \(PG(2,q)\) ⋮ On complete caps in the projective geometries over \(\mathbb F_3\) ⋮ Caps on classical varieties and their projections ⋮ New inductive constructions of complete caps inPG(N, q),qeven ⋮ Small complete caps from singular cubics. II ⋮ Recursive constructions of complete caps ⋮ The geometric description of a cyclic \((q- \sqrt{q}+1)\)-arc in \(\text{PG} (q-\sqrt{q}-3,q)\), \(q\) square ⋮ Existence of canonically inherited arcs in Moulton planes of odd order ⋮ Linear codes with covering radius 3 ⋮ Open problems in finite projective spaces ⋮ On proper secrets, \((t,k)\)-bases and linear codes ⋮ Upper bounds on the smallest size of a complete cap in $\mathrm{PG}(N,q)$, $N\ge3$, under a certain probabilistic conjecture ⋮ On sizes of complete caps in projective spaces \(\mathrm{PG}(n, q)\) and arcs in planes \(\mathrm{PG}(2, q)\) ⋮ New bounds for linear codes of covering radii 2 and 3 ⋮ Computer search for small complete caps ⋮ New covering codes of radius \(R\), codimension \(tr\) and \(tr+\frac{R}{2}\), and saturating sets in projective spaces ⋮ On the largest caps contained in the Klein quadric of \(PG(5,q)\), \(q\) odd ⋮ A family of caps in projective 4-space in odd characteristic ⋮ Upper bounds on the smallest size of a complete arc in \(\mathrm{PG}(2, {q})\) under a certain probabilistic conjecture
Cites Work
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- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Almost MDS codes
- On the completeness of certain plane arcs. II
- Curve razionali normali e \(k\)-archi negli spazi finiti
- Le geometrie di Galois
- On the uniqueness of \((q+1)_ 4\)-arcs of \(PG(4,q),q=2^ h,h\vee\)
- New examples of complete k-arcs in PG(2,q)
- A class of \(((p^ n-p^ m)(p^ n-1)\), \(p^ n-p^ m)\)-arcs in \(PG(2,p^ n)\)
- Arcs in projective planes over prime fields
- Ovoids of PG(3,16) are elliptic quadrics
- Quasiperfect linear binary codes with distance 4 and complete caps in projective geometry
- Small complete arcs in Galois planes
- The non-classical 10-arc of PG(4,9)
- On the sharpness of a theorem of B. Segre
- Complete arcs and algebraic curves in \(\text{PG}(2,q)\)
- Note on the order of magnitude of k for complete k-arcs in PG(2,q)
- On the completeness of certain plane arcs
- Ovoides et groupes de Suzuki
- The solution to Beniamino Segre's problem \(I_ p,\),p=3, q=\(2^ k\).
- Constructions of large arcs and blocking sets in finite planes
- Polynomial multiplicities over finite fields and intersection sets
- Note on the existence of large minimal blocking sets in Galois planes
- A new hyperoval in \(PG(2,32)\)
- Ovoids of \(PG(3,16)\) are elliptic quadratics. II
- Complete \(k\)-arcs in PG(\(n,q\)), \(q\) even
- M.D.S. codes and arcs in \(\mathrm{PG}(n,q)\) with \(q\) even: an improvement of the bounds of Bruen, Thas, and Blokhuis
- Caps in \(\mathrm{PG}(n,q)\), \(q\) even, \(n\ge 3\)
- On the existence of finite chain-m-structures and k-arcs in finite projective spaces
- Some results concerning \(\{(q+1)(n-1);\;n\}\)-arcs and \(\{(q+1)\;(n-1)+1;\;n\}\)-arcs in finite projective planes of order \(q\)
- Ovals in the Desarguesian plane of order 16
- Blocking sets
- Lower bounds on \(m_t(r,s)\)
- Caps and codes
- \(\alpha\)-flocks and hyperovals
- \(k\)-arcs and dual \(k\)-arcs
- On the size of a blocking set in \(\text{PG}(2,p)\)
- On multiple nuclei and a conjecture of Lunelli and Sce
- Classification of ovoids in \(PG(3,32)\)
- Classification of hyperovals in \(PG(2,32)\)
- Caps in finite projective spaces of odd order
- Maximal arcs in Desarguesian planes of odd order do not exist
- Complete arcs
- Proper blocking sets in projective spaces
- Small complete caps in \(PG(r,q)\), \(r\geq 3\)
- Classical arcs in \(PG(r,q)\) for \(11\leq q\leq 19\)
- On the size of a double blocking set in \(\text{PG}(2,q)\)
- On the embedding of an arc into a conic in a finite plane
- A characterization of some \([n,k,d;q\)-codes meeting the Griesmer bound using a minihyper in a finite projective geometry]
- Linear independence in finite spaces
- Classical arcs in PG\((r,q)\) for \(23\leq q\leq 29\)
- Isomorphisms between Subiaco \(q\)-clan geometries
- A tensor product action on \(q\)-clan generalized quadrangles with \(q=2^ e\)
- On near-MDS codes
- On hyperovals in small projective planes
- Flocks and ovals
- Arcs in \(\mathrm{PG}(n,q)\) fixed by \(A_5\) and \(A_6\)
- Small complete caps in spaces of even characteristic
- On the size of a triple blocking set in \(\text{PG} (2,q)\)
- Classification of maximal caps in PG(3,5) different from elliptic quadrics
- A class of complete \(k\)-caps in \(PG(3,q)\) for \(q\) an odd prime
- Hyperovals in PG(2,16)
- Linear codes with covering radius 2 and other new covering codes
- A family of complete arcs in finite projective planes
- Covering radius---Survey and recent results
- On the maximum sizes of certain (k, n)-arcs in finite projective geometries
- Caps in Elliptic Quadrics
- On the uniqueness of (q + 1)-arcs of PG (5, q), q = 2h, h ≥ 4
- An elementary proof and an extension of Thas' theorem on k-arcs
- Multiple Blocking Sets and Arcs in Finite Planes
- Ovoids and Translation Ovals
- On Pellegrino's 20-Caps in S4, 3
- The automorphism group of a complete (q − 1)‐arc in PG(2,q)
- On the size of arcs in projective spaces
- Weighted coverings and packings
- Algebraically punctured cyclic codes
- Some maximal arcs in finite projective planes
- Abelian varieties over finite fields
- Baer subplanes and blocking sets
- A Bound for Error-Correcting Codes
- Blocking Sets in Finite Projective Planes
- On a Bound Useful in the Theory of Factorial Designs and Error Correcting Codes
- Orthogonal Arrays of Index Unity
- Ovals In a Finite Projective Plane
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