Asymmetric Binary Covering Codes

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Asymmetric Binary Covering Codes
An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Qn such that every vector x Qn can be obtained from some vector c C by changing at most R 1's of c to 0's, where R is as small as possible. K+ (n, R) is defined as the smallest size of such a code. We show K+ (n, R) (2n /nR ) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K+ (n, n-R) = R+1 for constant coradius R iff n R(R+1)/2. These two results are extended to near-constant R and R, respectively. Various bounds on K+ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n, R]+ -code) is determined to be min{0, n - R}. We conclude by discussing open problems and techniques to compute explicit values for K+ , giving a table of best known bounds.
Joshua N. Cooper, Robert B. Ellis, Andrew B. Kahng
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JCT
Authors Joshua N. Cooper, Robert B. Ellis, Andrew B. Kahng
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