Some constructions of superimposed codes in Euclidean spaces
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Flat tori, lattices and bounds for commutative group codes
Designs, Codes and Cryptography
A set of triphase coded waveforms: design, analysis and application to radar system
MILCOM'09 Proceedings of the 28th IEEE conference on Military communications
Optimized punctured ZCZ sequence-pair set: design, analysis, and application to radar system
EURASIP Journal on Wireless Communications and Networking - Special issue on radar and sonar sensor networks
| Hi-index | 754.84 |
We use linear programming techniques to obtain new upper bounds on the maximal squared minimum distance of spherical codes with fixed cardinality. Functions Qj(n,s) are introduced with the property that Qj(n,s)<0 for some j>m if and only if the Levenshtein bound Lm(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⩾5 there exists a constant k=k(n) such that all Levenshtein bounds Lm(n, s) for m⩾2k-1 can be improved. An algorithm for obtaining new bounds is proposed and discussed