TR#: | CS0827 |
Class: | CS |
Title: | ON COVERING PROBLEMS OF CODES. |
Authors: | M. Frances and A. Litman |
CS0827.pdf | |
Abstract: | Let C be a binary code of length n. The Radius of C is the smallest integer r such that C is contained in an r-radius ball in the Hamming metric space <\{0,1\}^n,d>. The Covering Radius of C is the smallest integer r such that each vector in \{0,1\}^n is at a distance at most r from some code word. We show that the problems of computing the Radius and the Covering Radius of an arbitrary binary code are both NP complete. A central tool in our work is an intriguing characterization of the following set of binary vectors of length 2n: \{v=v_1,v_2 \cdots v_{2n}|v_{2i} = v_{2i-1} \forall i=1,...,n\} (doubled vectors). We show that there is a specific set Y of O(n) vectors such that the doubled vectors are exactly the centers of all n-radius spheres which contains Y. |
Copyright | The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information |
Remark: Any link to this technical report should be to this page (http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/1994/CS/CS0827), rather than to the URL of the PDF files directly. The latter URLs may change without notice.
To the list of the CS technical reports of 1994
To the main CS technical reports page