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An improved sphere covering bound for the codes with n=3 R+2

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1 Author(s)
X. -D. Hou ; Dept. of Math., Illinois Univ., Chicago, IL, USA

Let C be a binary code (not necessarily linear) with covering radius R and length n=3R+2. The sphere covering bound on the cardinality of C is improved considerably provided C has minimal distance d>2. Some new results on the function t[n,k] (the smallest covering radius of any binary linear code with length n and dimension k): t[38.6]⩾13, t[47.7]⩾16, t[59.8]⩾20 are given

Published in:

IEEE Transactions on Information Theory  (Volume:36 ,  Issue: 6 )