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|Title:||An investigation of the tangent splash of a subplane of PG(2,q3)|
|Citation:||Designs, Codes and Cryptography, 2015; 76(3):451-468|
|S. G. Barwick, Wen-Ai Jackson|
|Abstract:||In PG(2,q3), let π be a subplane of order q that is tangent to ℓ∞. The tangent splash of π is defined to be the set of q2+1 points on ℓ∞ that lie on a line of π. 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 PG(2,q3) in PG(6,q). We show that a tangent splash of PG(1,q3) is a GF (q)-linear set of rank 3 and size q2+1; 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.|
|Description:||Received: 12 May 2013 / Revised: 23 March 2014 / Accepted: 8 April 2014 / Published online: 3 May 2014|
|Rights:||© Springer Science+Business Media New York 2014|
|Appears in Collections:||Mathematical Sciences publications|
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