On the fabulous (11, 5, 2) Biplane

• Main Authors: Alulod, Ma. Monelette Zen M., Leyesa, Khristine Audrey A.
• Format: text
• Language: English
• Published: Animo Repository 2009
• Subjects: Biplanes; Combinatorial designs and configurations; Coding theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/6379
• Institution: De La Salle University

This thesis is an exposition of the article entitled The Fabulous (11, 5, 2) Biplane by Ezra Brown which appeared in the Mathematics Magazine Vol. 77, No. 2, on April 2004. The (11, 5, 2) biplane is a symmetric 2-design with 11 points and 11 blocks. Each block contains 5 points and every pair of points are contained in 2 blocks. This thesis discusses the properties of the (11, 5, 2) biplane as a symmetric design. It also computes the order of automorphism group of the (11, 5, 2) biplane. It gives the relationship of the (11, 5, 2) biplane with other combinatorial objects. In particular, it shows how the (11, 5, 2) biplane can be constructed from the binary Golay codes G24 and G23 and the ternary Golay codes G12 and G11, and vice-versa. This thesis also presents how the Steiner systems S(5, 6, 12) and S(4, 5, 11) can be constructed from the (11, 5, 2) biplane. The thesis also describes how the Steiner systems S(5, 8, 24) and S(4, 7, 23) can be constructed from the Golay code G24.