This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides the only comprehensive treatise on this area of mathematics. This new edition is a complete reworking, containing extensive revisions. Part I gives a survey of finite fields and an outline of ...
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This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides the only comprehensive treatise on this area of mathematics. This new edition is a complete reworking, containing extensive revisions. Part I gives a survey of finite fields and an outline of the fundamental properties of projective spaces and their automorphisms. Part II covers, in an arbitrary dimension, the properties of subspaces, of partitions into both subspaces and subgeometires, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed acount of the line and plane. This volume is an invaluable resource for researchers in finite geometry, combinatorics, and coding theory.
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