An investigation of the tangent splash of a subplane of

作者：Barwick S G^*; Jackson Wen Ai

来源：Designs, Codes and Cryptography, 2015, 76(3): 451-468.

DOI：10.1007/s10623-014-9971-3

• Bruck-Bose representation
• Cubic extension
• Subplanes
• Sherk surfaces
• Cover planes
• Linear sets

In , let be a subplane of order that is tangent to . The tangent splash of is defined to be the set of points on that lie on a line of . This article investigates properties of the tangent splash. We show that all tangent splashes are projectively equivalent, investigate sublines contained in a tangent splash, and consider the structure of a tangent splash in the Bruck-Bose representation of in . We show that a tangent splash of is a -linear set of rank 3 and size ; this allows us to use results about linear sets from Lavrauw and Van de Voorde (Des. Codes Cryptogr. 56:89-104, 2010) to obtain properties of tangent splashes.

• 出版日期2015-9