Article

Designs, Codes and Cryptography

, Volume 5, Issue 1, pp 57-72

First online:

The translation planes of order 49

  • Rudolf MathonAffiliated withDepartment of Computer Science, University of Western Australia
  • , Gordon F. RoyleAffiliated withDepartment of Computer Science, University of Toronto

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Abstract

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.