Introduction and Table of Contents


by E. F. Assmus, Jr. and J. D. Key

Designs and their Codes described the association of linear error-correcting codes with designs and collected together many of the significant known results. Recall that the linear p-ary code associated with a design D is equivalent to the row space over the finite field GF(p) of an incidence matrix for D with rows indexed by the blocks of D, and columns indexed by the points. Various classes of designs were discussed in the book and the corresponding results concerning the codes were described and established. A second printing --- with corrections but substantially unchanged --- appeared in 1993; here we will review some of the classes of designs discussed in the book --- updating the results --- and also examine further cases not covered there. We arrange this survey into the following ten sections:

  1. Introduction

  2. Basic definitions and terminology

  3. Projective and affine planes

  4. Oval designs

  5. Hadamard designs

  6. Unitals

  7. Steiner triple systems

  8. Finite geometries and rigidity theorems

  9. Dual structures and the ``point'' code of a design

  10. Strongly regular graphs and their p-ranks

E. F. Assmus, Jr.
Home Page
PhD Students