Some new lower bounds for binary and ternary covering codes

A modified lower bound for binary codes with covering radius one is derived. Let K_q(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