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Some new lower bounds for binary and ternary covering codes

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1 Author(s)
G. J. M. van Wee ; Philips Res. Lab., Eindhoven, Netherlands

A modified lower bound for binary codes with covering radius one is derived. Let Kq(n,R) denote the minimum cardinality of a q-ary code with covering radius R . The new bound shows that K2(11,1)⩾177 and that K2(17,1)⩾7391, improvements of the best lower bounds known. The authors also generalize a known lower bound for binary codes to the case of arbitrary q. For q=3, this simple bound improves the best lower bounds known in several cases. An updated version of a table for K3(n,R ) is included

Published in:

IEEE Transactions on Information Theory  (Volume:39 ,  Issue: 4 )