On some transitive combinatorial structures constructed from the unitary group U(3,3)

Crnković, Dean; Crnković, Vedrana Mikulić; Švob, Andrea

doi:10.1016/j.jspi.2012.05.006

Cited by 15 publications

(19 citation statements)

References 2 publications

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“…The method that allows a construction of all 1-designs such that G acts primitively on the point set and the block set of the design, including designs that have a point stabilizer and a block stabilizer that are not conjugate, is given in [10].…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…Strongly regular graphs constructed from the support designs of the codes of small dimension Up to isomorphism, we constructed 9 strongly regular graphs and their complements. The strongly regular graphs with parameters (21,10,3,6), (49, 12, 5, 2), (56, 10, 0, 2), (105,32,4,12), (112,30,2,10) and (120,42,8,18) are unique, up to isomorphism (see [5]). The graph with parameters (28,12,6,4) is the triangular graph T (8).…”

Section: Strongly Regular Graphs Constructed From the Support Designsmentioning

confidence: 99%

“…Moreover, we give the full weight distribution of these codes, describe the nature of the minimum weight codewords, and the structure of the stabilizer of a word in this weight class. It is a result of [19], (see also [10,22,21]) that if we form any union of orbits of the stabilizer of a point, including the orbit consisting of the single point, and orbit this under the full group, we will obtain a symmetric design with the group acting on.…”

Section: Introductionmentioning

confidence: 99%

“…Using this method we construct self-orthogonal codes corresponding to the respective weakly self-orthogonal designs. Furthermore, from the support designs of these codes we construct strongly regular graphs with parameters (21,10,3,6), (28,12,6,4), (49,12,5,2), (49,18,7,6), (56,10,0,2), (63, 30,13,15), (105,32,4,12), (112,30,2,10) and (120,42,8,18).…”

Section: Introductionmentioning

confidence: 99%

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On self-orthogonal designs and codes related to Held's simple group

Crnković¹,

Crnković²,

Rodrigues³

2018

Advances in Mathematics of Communications

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A construction of designs acted on by simple primitive groups is used to find some 1-designs and associated self-orthogonal, decomposable and irreducible codes that admit the simple group He of Held as an automorphism group. The properties of the codes are given and links with modular representation theory are established. Further, we introduce a method of constructing self-orthogonal binary codes from orbit matrices of weakly self-orthogonal designs. Furthermore, from the support designs of the obtained self-orthogonal codes we construct strongly regular graphs with param

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Section: Preliminary Resultsmentioning

confidence: 99%

Section: Strongly Regular Graphs Constructed From the Support Designsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On self-orthogonal designs and codes related to Held's simple group

Crnković¹,

Crnković²,

Rodrigues³

2018

Advances in Mathematics of Communications

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“…The graphs obtained in this paper are constructed using the method described in [9] which can be rewritten in terms of coherent configurations in the following way. Using this method one can construct all regular graphs admitting a transitive action of the group G. We will be interested only in those regular graphs that are distance-regular, and especially strongly regular.…”

Section: Srgs and Drgs Constructed From The Groupsmentioning

confidence: 99%