## Coding Theory and Design Theory: Coding theory, Volume 1These books are based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on Applied Combinatorics. Coding Theory and Design theory are areas of combinatorics which found rich applications of algebraic structures and are closely interconnected. Coding theory has developed into a rich and beautiful example of abstract sophisticated mathematics being applied successfully to solve real-life problems of communication. |

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### Contents

Baer subplanes ovals and unitals | 1 |

Automorphism groups of block structures with | 7 |

The differential encoding of coset codes by algebraic methods | 16 |

Copyright | |

15 other sections not shown

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### Common terms and phrases

abelian group algebra array association scheme binary Calderbank called cell character table character theory codewords coding theory coefficients columns computation conjugacy classes contained coordinates Corollary corresponding coset covering radius curve defined Definition denote dimension distance divisor eigenvalues elements equation equivalent Euclid's algorithm example exists finite function geometric codes given Goppa codes graded poset group G Hamming schemes Hermitian variety hyperplane idempotent incidence algebra incidence matrix input integer intersects isomorphic Lemma length loop Math Mathematics maximal metric scheme minimum number of points obtained pairs parameters partial perfect codes perfect multiple coverings permutation PMC with radius polar polynomial division Proof Proposition quadric quasigroup rank rational points rN(x rT(x satisfies scalar Section self-dual sequence Spin(n strongly regular graph subgroups subsets subspace Suppose symmetric tangent Theorem trellis code uniform clutter uniform poset vector space vertex Vjv-i weight zero