Constructing transitive permutation groups

Hulpke, Alexander

doi:10.1016/j.jsc.2004.08.002

Cited by 71 publications

(42 citation statements)

References 21 publications

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“…The transitive permutation groups have been classified up to degree 32, see [5,23] (and this work has recently been extended to degree 47), so these groups are readily available. For (ii), we first use standard Magma functions to find the conjugacy classes of elements of order v in G, then we select those that consist of a single v-cycle, and hence generate a regular cyclic subgroup, and finally we test the subgroups that they generate for conjugacy in G. If there is more than one conjugacy class in G of regular cyclic subgroups, then we proceed to (iii).…”

Section: Isomorphisms Of Cyclic Steiner Quadruple Systemsmentioning

confidence: 99%

“…By the discussion after Theorem 3, there are exactly 4 isomorphism classes of affine-invariant CSQS(26)s. Number = 51 Order = 392 Generators: (1,8,14,20,25,4,10,15,22,27,5,12,17,23,2,7,13,19,26,3,9,16,21,28,6,11,18,24 (20,24), (1,11,7,4,14,10,6,2,12,8,3,13,9,5), (1,21,14,24,12,25,9,28,7,15,6,17,3,20) (2,22,13,23,11,26,10,27,8,16,5,18,4,19 (9,20,10,19) (11,<...>…”

Section: Related Designsmentioning

confidence: 99%

“…Number = 249 Order = 3528 Generators: (1,5)(2,6)(3,4) (7,23,20,27,12,16) (8,24,19,28,11,15)(9,26)(10,25)(13,21)(14,22)(17,18), (1,24,14,19,25,15,10,11,22,7,5,4,17,28,2,23,13,20,26,16,9,12,21,8,6,3,18,27). Number = 326 Order = 7056 Generators: (1,13)(2,14)(3,11)(4,12)(5,9)(6,10)(7,8) (17,21,20,28,24,25) (18,22,19,27,23,26), (1,22,7,26,14,16,6,19,12,23,3,27,9,18) (2,21,8,25,13,15,5,20,11,24,4,28,10,17), (1,…”

Section: Related Designsmentioning

confidence: 99%

See 2 more Smart Citations

Classification of Cyclic Steiner Quadruple Systems

et al. 2016

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The problem of classifying cyclic Steiner quadruple systems (CSQSs) is considered. A computational approach shows that the number of isomorphism classes of such designs with orders 26 and 28 is 52170 and 1028387, respectively. It is further shown that CSQSs of order 2p, where p is a prime, are isomorphic iff they are multiplier equivalent. Moreover, no CSQSs of order less than or equal to 38 are isomorphic but not multiplier equivalent.

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Section: Isomorphisms Of Cyclic Steiner Quadruple Systemsmentioning

confidence: 99%

Section: Related Designsmentioning

confidence: 99%

Section: Related Designsmentioning

confidence: 99%

See 1 more Smart Citation

Classification of Cyclic Steiner Quadruple Systems

et al. 2016

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“…Magma contains a database of all transitive groups with degree at most 30. This is based on one constructed by Hulpke [14] making use of a classification by Butler and McKay for degree at most 15. Usually the largest two or three groups with internal minimum distance at least d were considered.…”

Section: Automorphism Groupsmentioning

confidence: 99%

A new table of permutation codes

Smith

Montemanni

2011

Des. Codes Cryptogr.

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Permutation codes (or permutation arrays) have received considerable interest in recent years, partly motivated by a potential application to powerline communication. Powerline communication is the transmission of data over the electricity distribution system. This environment is rather hostile to communication and the requirements are such that permutation codes may be suitable. The problem addressed in this study is the construction of permutation codes with a specified length and minimum Hamming distance, and with as many codewords (permutations) as possible. A number of techniques are used including construction by automorphism group and several variations of clique search based on vertex degrees. Many significant improvements are obtained to the size of the best known codes.

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“…Other examples of the use of the soluble radical algorithm follow. The group T is TransitiveGroup(30, 2000) from MAGMA's collection of transitive permutation groups, supplied by Hulpke [11]. The timings of the sequence of subgroups of AGL 7 (3) A 5 shows the influence of a refinement to the blocks kernel algorithm not mentioned above.…”

Section: Timingsmentioning

confidence: 99%