# American Institute of Mathematical Sciences

February  2007, 1(1): 131-149. doi: 10.3934/amc.2007.1.131

## Codes in spherical caps

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

Received  June 2006 Revised  August 2006 Published  January 2007

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.
Citation: Alexander Barg, Oleg R. Musin. Codes in spherical caps. Advances in Mathematics of Communications, 2007, 1 (1) : 131-149. doi: 10.3934/amc.2007.1.131
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