## Contributions to the Simplex Code Conjecture |

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### Contents

INTRODUCTION | 1 |

A SIMPLIFIED PROOF OF LANDAU AND SLEPIANS INEQUALITY | 11 |

SOME NEW FORMULATIONS | 31 |

1 other sections not shown

### Common terms and phrases

angle Q arbitrary assume Balakrishnan ball density conjecture center of mass Chapter circle Communications Theory constraint contain the origin convex hull convex region correct decoding define denote differential element dimensional content Farber Fejes-Toth theorem function corresponding Gaussian noise geometric global optimality hyper hypersphere of radius implies induction hypothesis inequality integral K°Cne Landau and Slepian Lemma linearized version mathematical maximize the intersection maximizes the mean mean width minimizes monotone decreasing function n-2)-dimensional content n-dimensional n-dimensions n-l)-dimensional n+l n+1 noise function optimum polytope probability density function probability of error problem prove r)dr r+Ar regular simplex maximizes Shannon signal set signal-to-noise ratios simplex code conjecture simplex conjecture simplicial cone simplified proof single hyperplane solid angle sphere spherical cap spherical projection spherical simplex subspace surface tetrahedron thesis unique unit hypersphere v(r+Ar vertices volume x)dx Z Z Z zero