1995
DOI: 10.1137/s0895480193252100
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Bounds for Binary Codes that are Multiple Coverings of the Farthest-Off Points

Abstract: A binary code C C_ ] with M codewords is called an (n, M, r, it) multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole space ] and. every x E ] such that d(x, C) r is covered by at least it codewords.The minimum possible cardinality F(n, r, it) of such a code is studied and tables of upper bounds on F(n, r, it) for n _ 16, r _ 4, it _ 4 are given.

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Cited by 10 publications
(11 citation statements)
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“…• Multiple coverings of the farthest-off points (MCF) [26]: mi = 1 for i = 0, 1, ... , 6-1, m 6 = 1/j, where j is a positive integer.…”
Section: Notations and Known Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…• Multiple coverings of the farthest-off points (MCF) [26]: mi = 1 for i = 0, 1, ... , 6-1, m 6 = 1/j, where j is a positive integer.…”
Section: Notations and Known Resultsmentioning
confidence: 99%
“…Assume that a(l), . [26) the words of weights 0, 2, 5 and 7 in F 7 form a (1, 1/3)-covering. In fact, the density of this covering is equal to 1 at all except the 14 points that have weight 1 or 6, at which the density is 7/3.…”
Section: Matrix Constructionmentioning
confidence: 99%
See 2 more Smart Citations
“…In [6,18,19,23,24,28,29] results on MCF codes, mostly concerning the binary and the ternary cases, can be found. The development of this topic for arbitrary q was presented in [2,15,27] and in the recent paper [3].…”
Section: Introductionmentioning
confidence: 99%