On the fabulous (11, 5, 2) biplane

Date of Publication

2009

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Blessilda P. Raposa

Defense Panel Chair

Ederlina G. Nocon

Defense Panel Member

Arlene A. Pascasio

Abstract/Summary

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."

Abstract Format

html

Language

English

Format

Print

Accession Number

TU15134

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

vi, 106, 87-100 leaves, illustrations, 28 cm.

Keywords

Biplanes; Combinatorial designs and configurations; Block designs; Coding theory

Embargo Period

3-30-2021

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