Designs over finite fields

Thomas, Simon

doi:10.1007/bf00150939

Cited by 86 publications

(78 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…q−analogues of designs were introduced by Thomas in 1987 [19]. Later they were studied in a paper by Braun et al [7] were the authors constructed the first non-trivial q−analogue of a 3−design.…”

Section: Q−analogues Of Designsmentioning

confidence: 99%

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Kohnert

Kurz

2008

Mathematical Methods in Computer Science

127

160

View full text Add to dashboard Cite

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

show abstract

Section: Q−analogues Of Designsmentioning

confidence: 99%

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Kohnert

Kurz

2008

Mathematical Methods in Computer Science

127

160

View full text Add to dashboard Cite

show abstract

“…Furthermore, two examples of 2 - (7,3,3; 2) designs admitting the normalizer of a Singer cycle were found by the second author [ 111, during the enumeration of equivalence classes of nontrivial 2 -(7,3,3; 2) designs admitting Singer cycles. The nonexistence of 2 -(7,3,1; 2) designs admitting Singer cycles was reported in [16]. T. Itoh proved in his master's thesis [7] that there is no nontrivial 2 -(6,3, A; 2) design admitting a Singer cycle for any A.…”

Section: Introductionmentioning

confidence: 98%

On a class of small 2‐designs over gf(q)

Miyakawa

Munemasa

Yoshiara

1995

J of Combinatorial Designs

View full text Add to dashboard Cite

A 2 -(v,k,A;q) design is a pair (V,23) of a v-dimensional vector space V over GF(q) and a collection 23 of k-dimensional subspaces of V such that each 2-dimensional subspace of V is contained in exactly A members of 23. Assuming transitivity of their automorphism groups on the nonzero vectors of V, we give a classification of nontrivial such designs for v = 7, q = 2,3 with small A, together with the nonexistence proof of those designs for v 5 6.0 1995

show abstract

“…The first nontrivial subspace design with t = 2 has been constructed in [39] and the first one with t = 3 in [7]. More constructions based on the method of [32,7] have been presented in [8,11].…”

mentioning

confidence: 99%

“…To our knowledge, besides [15] the only known infinite series of nontrivial subspace designs with t ≥ 2 so far are the following: In [39] a series of 2-designs was constructed for q = 2 and generalized to all prime powers q in [35] and [36]. Based on these designs, the recursive construction in [22] provides further 2-designs.…”

mentioning

confidence: 99%

Large sets of subspace designs

Braun

Kiermaier

Kohnert³

et al. 2017

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

Abstract. In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Graßmannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs.We construct a 2-(6, 3, 78) 5 design by computer, which corresponds to a halving LS 5 [2](2, 3, 6). The application of the new recursion method to this halving and an already known LS 3 [2](2, 3, 6) yields two infinite two-parameter series of halvings LS 3 [2](2, k, v) and LS 5 [2](2, k, v) with integers v ≥ 6, v ≡ 2 (mod 4) and 3Thus in particular, two new infinite series of nontrivial subspace designs with t = 2 are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with t = 2.

show abstract

Designs over finite fields

Cited by 86 publications

References 2 publications

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance

On a class of small 2‐designs over gf(q)

Large sets of subspace designs

Contact Info

Product

Resources

About