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Conway groupoids and completely transitive codes

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posted on 2018-01-29, 17:35 authored by Nick Gill, Neil I. Gillespie, Jason Semeraro
To each supersimple 2−(n,4,λ) design D one associates a ‘Conway groupoid’, which may be thought of as a natural generalisation of Conway’s Mathieu groupoid M13 which is constructed from P3. We show that Sp2m(2) and 22m.Sp2m(2) naturally occur as Conway groupoids associated to certain designs. It is shown that the incidence matrix associated to one of these designs generates a new family of completely transitive F2-linear codes with minimum distance 4 and covering radius 3, whereas the incidence matrix of the other design gives an alternative construction of a previously known family of completely transitive codes. We also give a new characterization of M13 and prove that, for a fixed λ > 0, there are finitely many Conway groupoids for which the set of morphisms does not contain all elements of the full alternating group.

History

Citation

Combinatorica, 2017

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Combinatorica

Publisher

Springer Verlag (Germany) for János Bolyai Mathematical Society

issn

0209-9683

eissn

1439-6912

Copyright date

2017

Available date

2018-02-13

Publisher version

https://link.springer.com/article/10.1007/s00493-016-3433-7

Notes

Mathematics Subject Classification (2010): 20B15, 20B25, 05B05;The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en

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