Abstract
The Leech lattice is a regular arrangement of points in 24-dimensional Euclidean space that yields an extremely dense packing when equal spheres are centered at these points. A subset of the Leech lattice can be used as a signal set for the Gaussian channel or as representative vectors for a vector quantizer. Of particular interest are the spherical codes (or code books) that consist of the points of the Leech lattice which lie on a sphere centered at the origin. The code points do not have to be stored because they can be obtained from a very small set of basic vectors using permutations of the components in a manner dictated by the words of the extended Golay code. A nearest-neighbor algorithm that works on this is developed to determine the point in the code closet to some arbitrary vector in R/sup 24/. The performance of this approach when quantizing independent identically distributed Gaussian samples is reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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