Conway Groupoids and Completely Transitive Codes

  title={Conway Groupoids and Completely Transitive Codes},
  author={Nick Gill and Neil I. Gillespie and Jason Semeraro},
  • Nick Gill, Neil I. Gillespie, Jason Semeraro
  • Published 2018
  • Mathematics, Computer Science
  • Combinatorica
  • 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… CONTINUE READING

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