DocumentCode
942117
Title
Further results on the covering radius of codes
Author
Cohen, Gerard D. ; Lobstein, Antoine C. ; Sloane, N. J A
Volume
32
Issue
5
fYear
1986
fDate
9/1/1986 12:00:00 AM
Firstpage
680
Lastpage
694
Abstract
A number of upper and lower bounds are obtained for 
, the minimal number of codewords in any binary code of length 
and covering radius 
. Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This construction works best when applied to normal codes, and we give some new and stronger conditions which imply that a linear code is normal. An upper bound is given for the density of a covering code over any alphabet, and it is shown that 
holds for sufficiently large .
, the minimal number of codewords in any binary code of length and covering radius . Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This construction works best when applied to normal codes, and we give some new and stronger conditions which imply that a linear code is normal. An upper bound is given for the density of a covering code over any alphabet, and it is shown that holds for sufficiently large .Keywords
Coding/decoding; Binary codes; Error correction codes; Helium; Linear code; Upper bound;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.1986.1057227
Filename
1057227
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