The discovery of simple 7-designs with automorphism group PΓL(2, 32)

Betten, Anton; Kerber, Adalbert; Kohnert, Axel; Laue, Reinhard; Wassermann, Alfred

doi:10.1007/3-540-60114-7_10

Cited by 20 publications

(36 citation statements)

References 11 publications

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“…This construction method is a general approach that works for many discrete structures as designs [14,3], q-analogs of designs [6,7], arcs in projective geometries [8], linear codes [2,4,5,15] or quantum codes [21].…”

Section: Constant Dimension Codes With Prescribed Automorphismsmentioning

confidence: 99%

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Kohnert

Kurz

2008

Mathematical Methods in Computer Science

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In this paper we construct constant dimension space codes with prescribed minimum distance. There is an increased interest in space codes since a paper [13] by Kötter and Kschischang were they gave an application in network coding. There is also a connection to the theory of designs over finite fields. We will modify a method of Braun, Kerber and Laue [7] which they used for the construction of designs over finite fields to do the construction of space codes. Using this approach we found many new constant dimension spaces codes with a larger number of codewords than previously known codes. We will finally give a table of the best found constant dimension space codes. network coding, q-analogue of Steiner systems, subspace codes

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Section: Constant Dimension Codes With Prescribed Automorphismsmentioning

confidence: 99%

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Kohnert

Kurz

2008

Mathematical Methods in Computer Science

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126

160

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“…The construction of discrete objects using incidence preserving group actions [13] is a general approach that works in many other cases like designs [2,14], q-analogs of designs [6], parallelisms in projective geometries [5] .…”

Section: Related Workmentioning

confidence: 99%

Construction of (n,r)-arcs in PG(2,q)

Braun¹,

Kohnert²,

Wassermann³

2005

Innov. Incidence Geom.

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“…We used the algorithm to find all 7-(33, The algorithm described in [1] produced a 32 × 97 matrix which is a permutation of the rows and columns of the matrix in [16], generated by another set of permutations. The method of [1] in its first version found only 1 solution for λ = 10.…”

Section: Resultsmentioning

confidence: 99%

“…For finding just one solution the algorithms are mostly randomized, for example simulated annealing, combinatorial optimization, local search [17], and lattice basis reduction [1,11,12,19]. See [17] for a survey.…”

Section: A Simple T-(v K λ) Design Exists With G ≤ Sym(x) As An Autmentioning

confidence: 99%