Codes in spherical caps

Alexander Barg; Oleg R. Musin

doi:10.3934/amc.2007.1.131

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2007, Volume 1, Issue 1: 131-149. Doi: 10.3934/amc.2007.1.131

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Codes in spherical caps

Alexander Barg^1, and
Oleg R. Musin^2,

1.
Dept. of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742
2.
Institute for Math. Study of Complex Systems, Moscow State University, Moscow

Received: June 2006

Revised: August 2006

Published: February 2007

Abstract / Introduction Related Papers Cited by

Abstract

We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are considered.
It is proved that the maximum size of codes in spherical caps for large dimensions is determined by the maximum size of spherical codes, so these problems are asymptotically equivalent.

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Mathematics Subject Classification: Primary: 94B65.

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