The projective and polar geometries that arise from a vector space
over a finite field are particularly useful in the construction of
combinatorial objects, such as latin squares, designs, codes and
graphs. This book provides an introduction to these geometries and
their many applications to other areas of combinatorics. Coverage
includes a detailed treatment of the forbidden subgraph problem
from a geometrical point of view, and a chapter on maximum distance
separable codes, which includes a proof that such codes over prime
fields are short. The author also provides more than 100 exercises
(complete with detailed solutions), which show the diversity of
applications of finite fields and their geometries. Finite Geometry
and Combinatorial Applications is ideal for anyone, from a
third-year undergraduate to a researcher, who wishes to familiarise
themselves with and gain an appreciation of finite geometry.
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