On cone representations of translation planes

✍ Scribed by David G. Glynn

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 537 KB
• Volume: 58
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00058-4

✦ Synopsis

Let F be a field of order q. It is known that an orthogonal array of the same order q has rank n over F if and only if it is represented as a cone cut by hyperplanes in n-dimensional space over F. Here we show that translation planes have a cone representation in (n + 1)-dimensional space over F, where n is the dimension of the plane over its kernel. If the plane is a semifield plane then the representation takes a particularly nice form. Rank 3 representations of Moulton planes are also briefly discussed.