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Download fileConway groupoids and completely transitive codes
journal contribution
posted on 2018-01-29, 17:35 authored by Nick Gill, Neil I. Gillespie, Jason SemeraroTo 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, 2017Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- AM (Accepted Manuscript)