Designs, Codes and Cryptography

, Volume 5, Issue 1, pp 57–72

The translation planes of order 49

  • Rudolf Mathon
  • Gordon F. Royle

DOI: 10.1007/BF01388504

Cite this article as:
Mathon, R. & Royle, G.F. Des Codes Crypt (1995) 5: 57. doi:10.1007/BF01388504


In this paper, we describe an exhaustive computer search for all the translation planes of order 49. The search uses the well-known correspondence between translation planes of order 49 and spreads of lines inPG(3,7). We conclude that there are exactly 1347 translation planes of order 49, and give some of their properties including group sizes and 7-ranks.

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Rudolf Mathon
    • 1
  • Gordon F. Royle
    • 2
  1. 1.Department of Computer ScienceUniversity of Western AustraliaNedlandsAustralia
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada