Upper bounds on the minimum distance of spherical codes

We use linear programming techniques to obtain new upper bounds on the maximal squared minimum distance of spherical codes with fixed cardinality. Functions Q/sub j/(n,s) are introduced with the property that Q/sub j/(n,s)m if and only if the Levenshtein bound L/sub m/(n,s) on A(n,s)=max{|W|:W is an...

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Bibliographic Details
Published in:IEEE transactions on information theory 1996-09, Vol.42 (5), p.1576-1581
Main Authors: Boyvalenkov, P.G., Danev, D.P., Bumova, S.P.
Format: Article
Language:English
Subjects:
Codes
Combinatorial mathematics
Convolutional codes
Geometry
Information processing
Linear programming
Polynomials
Upper bound
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Summary:We use linear programming techniques to obtain new upper bounds on the maximal squared minimum distance of spherical codes with fixed cardinality. Functions Q/sub j/(n,s) are introduced with the property that Q/sub j/(n,s)m if and only if the Levenshtein bound L/sub m/(n,s) on A(n,s)=max{|W|:W is an (n,|W|,s) code} can be improved by a polynomial of degree at least m+1. General conditions on the existence of new bounds are presented. We prove that for fixed dimension n/spl ges/5 there exists a constant k=k(n) such that all Levenshtein bounds L/sub m/(n, s) for m/spl ges/2k-1 can be improved. An algorithm for obtaining new bounds is proposed and discussed.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.532903