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
Link To Document :
